comparisons of lattice boltzmann and finite difference methods for a two dimensional viscous burgers equation lattice boltzmann methods have been proposed as a computational means for solving various partial differential equations we look at three lattice boltzmann methods and an analogous finite difference method for solving a two dimensional scalar viscous burgers equation with periodic boundary conditions first using monotonicity arguments we prove that in the ell 1 norm the lattice boltzmann methods converge first order temporally and second order spatially then we provide some computational results which substantiate the theoretical results finally we compare the lattice boltzmann and finite difference methods the basis of comparison includes numerical results with regard to accuracy order of convergence performance and timing measurements memory requirements and conservations laws

lattice boltzmann model for two dimensional unsteady burgers equation in this paper a special lattice boltzmann model is proposed to simulate two dimensional unsteady burgers equation the maximum principle and the stability are proved the model has been verified by several test examples excellent agreement is obtained between numerical predictions and exact solutions the cases of steep oblique shock waves are solved and compared with the two point compact scheme results the study indicates that lattice boltzmann model is highly stable and efficient even for the problems with severe gradients

limit angular velocities of variable thickness rotating disks elastic and plastic limit angular velocities are calculated for rotating disks of variable thickness in power function form analytical solution is obtained and used to calculate elastic limit angular velocities of variable thickness rotating annular disks and annular disks with rigid inclusion an efficient numerical solution procedure is designed and used to obtain the elastic limit angular velocities of variable thickness rotating solid disks von mises yield criterion and its flow rule is used to estimate plastic limit angular velocities both linear and nonlinear hardening material behaviors are treated numerically the results are verified by comparing with those of uniform thickness rotating solid disks available in the literature elastic and plastic limit angular velocities are found to increase with the reduction of the disk thickness at the edge as well as the reduction in the disk mass due to the shape of the profile

a general algorithm for limit solutions of plane stress problems a computational approach to limit solutions is considered most challenging for two major reasons a limit solution is likely to be non smooth such that certain non differentiable functions are perfectly admissible and make physical and mathematical sense moreover the possibility of non unique solutions makes it difficult to analyze the convergence of an iterative algorithm or even to define a criterion of convergence in this paper we use two mathematical tools to resolve these difficulties a duality theorem defines convergence from above and from below the exact solution a combined smoothing and successive approximation applied to the upper bound formulation perturbs the original problem into a smooth one by a small parameter e as e 0 the solution of the original problem is recovered this general computational algorithm is robust such that from any initial trial solution the first iteration falls into a convex hull that contains the exact solution s of the problem unlike an incremental method thut invariably renders the limit problem ill conditioned the algorithm is numerically stable limit analysis itself is a highly efficient concept which bypasses the tedium of the intermediate elastic plastic deformation and seeks the most important information directly with the said algorithm we have produced many limit solutions of plane stress problems certain non smooth characters of the limit solutions are shown in the examples presented two well known as well as one parametric family of yield functions are used to allow comparison with some classical solutions

generalized petrov galerkin methods for the numerical solution of burgers equation generalized petrov galerkin methods are applied in two different ways for the numerical solution of burgers equation in the first place it is used to produce upwinding in the way described by mitchell and griffiths 9 10 the main objective of this paper is in the second place to use it as a moving finite element method in particular it is shown that the methods of miller and co workers4 6 and herbst et al 7 8 can be incorporated in the more general approach presented in this paper several choices for the test functions are discussed and numerical results are given

computation of limit loads for computing the collapse state of a perfect plastic continuum we suggest a mixed finite element approximation to the infinite dimensional mathematical programming problem of limit analysis the convergence of the limit load to the exact solution is discussed as well as solution methods for the discrete problem finally the method is applied to a classical problem in plane strain

a lattice boltzmann equation for waves we propose a lattice boltzmann model for the wave equation using a lattice boltzmann equation and the chapman enskog expansion we get 1d and 2d wave equations with truncation error of order two the numerical tests show the method can be used to simulate the wave motions

lattice boltzmann model for the modified burgers equation abstract in this paper a special lattice boltzmann model is developed to solve the modified burgers equation the maximum principle and the stability are proved the model has been verified by several test examples excellent agreement is obtained between numerical predictions and the constructed asymptotic solutions or available numerical results the careful numerical study indicates the computational efficiency and stability of the lattice boltzmann method

a steady state lattice boltzmann model for incompressible flows in this paper we propose a steady state lattice boltzmann equation which is independent of time for steady incompressible flows on the basis of the steady state lattice boltzmann equation we find a way of modeling some steady state problems using the lattice boltzmann model in further study we investigate steady state incompressible flows with the method of the higher order moment of equilibrium distribution functions and a series of partial differential equations for different space scales by assuming r constant we obtain the momentum equation for incompressible steady state flow the numerical results show that the new method is effective

a general algorithm for plastic flow simulation by finite element limit analysis abstract limit analysis has been rendered versatile in many structural and metal forming problems in metal forming analysis the slip line method and the upper bound method have filled the role of limit analysis as a breakthrough of the previous work a computational approach to limit solutions is considered as the most challenging area in the present work a general algorithm for limit solutions of plastic flow is developed with the use of finite element limit analysis the algorithm deals with a generalized holder inequality a duality theorem and combined smoothing and successive approximation in addition to a general procedure for finite element analysis the algorithm is robust such that from any initial trial solution the first iteration falls into a convex set which contains the exact solution s of the problem the idea of the algorithm for limit solutions is extended from rigid perfectly plastic materials to work hardening materials by the nature of the limit formulation which is also robust with numerically stable convergence and highly efficient computing time

a comparison of differential quadrature methods for the solution of partial differential equations abstract discrete ordinate methods for the solution of partial differential equations are examined and compared a novel approach for the discrete representation of differential operators based on split range polynomial expansions is introduced the utility of the method is demonstrated for the case of differentiation of functions involving steep gradients the solution of burgers equation is presented to illustrate the effectiveness of the technique for the solution of nonlinear partial differential equations exhibiting nearly discontinuous solutions comparisons are made with other differential quadrature methods

a fourth order numerical scheme for solving the modified burgers equation a finite difference scheme based on fourth order rational approximants to the matrix exponential term in a two time level recurrence relation is proposed for the numerical solution of the modified burgers equation the resulting nonlinear system which is analyzed for stability is solved using an already known modified predictor corrector scheme the results arising from the experiments are compared with the corresponding ones known from the available literature

a variational principle and an algorithm for limit analysis of beams and plates abstract a variational principle for limit analysis of beams and plates is developed from a yield function based on the frobenius matrix norm the formulation produced a pair of maximization and minimization problems with a duality relation between them exact solutions of two simple problems are presented as verification to the validity of the new variational principle an iterative algorithm is constructed to solve the minimization problem the algorithm tested successfully on the two example problems is intended for beams and plates with general loading and boundary conditions and shapes

a finite element approach for solution of burgers equation in this study for the burgers equation which is used a model problem in turbulence and shock wave theory was given a finite element solution considering the numerical results obtained for different values of viscosity compared with cole s analytical solution it was seen that they were in good agreement

a moving petrov galerkin method for transport equations a time dependent transport equation is solved numerically by using a petrov galerkin technique on a time dependent grid a piecewise linear trial solution and piecewise hermite cubic test functions are used the same method is also applied to a time independent problem in which case it automatically generates a grid in a way which bears some resemblance to certain existing grid generation techniques several numerical examples are given

on the numerical solution of nonlinear option pricing equation in illiquid markets abstract in this paper we focus on the numerical solution of nonlinear black scholes equation modeling illiquid markets two monotone unconditionally stable splitting methods ensuring positive numerical solution and avoiding unstable oscillations are applied to solve nonlinear black scholes equation modeling illiquid markets these numerical methods are based on the lod methods which allow us to solve the discrete equation explicitly the properties of these methods are analyzed the numerical results for vanilla call option are compared to the local crank nicolson scheme the numerical results for european butterfly spread are also provided

the approximate inverse in action ii convergence and stability the approximate inverse is a scheme for constructing stable inversion formulas for operator equations originally it is defined on l2 spaces in the present article we extend the concept of approximate inverse to more general settings which allow us to investigate the discrete version of the approximate inverse which actually underlies numerical computations indeed we show convergence if the discretization parameter tends to zero further we prove stability that is we show the regularization property finally we apply the results to the filtered backprojection algorithm in 2d tomography to obtain convergence rates

biorthogonal bases of compactly supported wavelets orthonormal bases of compactly supported wavelet bases correspond to subband coding schemes with exact reconstruction in which the analysis and synthesis filters coincide we show here that under fairly general conditions exact reconstruction schemes with synthesis filters different from the analysis filters give rise to two dual riesz bases of compactly supported wavelets we give necessary and sufficient conditions for biorthogonality of the corresponding scaling functions and we present a sufficient condition for the decay of their fourier transforms we study the regularity of these biorthogonal bases we provide several families of examples all symmetric corresponding to linear phase filters in particular we can construct symmetric biorthogonal wavelet bases with arbitrarily high preassigned regularity we also show how to construct symmetric biorthogonal wavelet bases close to a nonsymmetric orthonormal basis

moving mesh methods based on moving mesh partial differential equations several versions of a moving mesh method are developed based on a mesh spatial smoothing technique and on the moving mesh pdes derived in a previous paper these versions are quite simple and easy to program they are applied to three bench mark one dimensional problems which show different solution behaviour the numerical results clearly demonstrate that the present methods are capable of accurately tracking rapid spatial and temporal transitions

quadratic b spline finite element method for numerical solution of the burgers equation abstract in this paper the one dimensional nonlinear burgers equation was converted to a set of nonlinear ordinary differential equations by the method of discretization in time and then each of them was solved by applying the quadratic b spline finite element method in order to show the efficiency of the presented method two problems were considered the numerical solutions obtained for various values of viscosity were compared with the exact solutions it is seen that the results obtained by this way are quite satisfactory

a numerical study of three moving grid methods for one dimensional partial differential equations which are based on the method of lines in recent years several sophisticated packages based on the method of lines mol have been developed for the automatic numerical integration of time dependent problems in partial differential equations pdes notably for problems in one space dimension these packages greatly benefit from the very successful developments of automatic stiff ordinary differential equation solvers however from the pde point of view they integrate only in a semiautomatic way in the sense that they automatically adjust the time step sizes but use just a fixed space grid chosen a priori for the entire calculation for solutions possessing sharp spatial transitions that move e g travelling wave fronts or emerging boundary and interior layers a grid held fixed for the entire calculation is computationally inefficient since for a good solution this grid often must contain a very large number of nodes in such cases methods which attempt automatically to adjust the sizes of both the space and the time steps are likely to be more successful in efficiently resolving critical regions of high spatial and temporal activity methods and codes that operate this way belong to the realm of adaptive or moving grid methods following the mol approach this paper is devoted to an evaluation and comparison mainly based on extensive numerical tests of three moving grid methods for 1d problems viz the finite element method of miller and co workers the method published by petzold and a method based on ideas adopted from dorii and drury our examination of these three methods is aimed at assessing which is the most suitable from the point of view of retaining the acknowledged features of reliability robustness and efficiency of the conventional mol approach therefore considerable attention is paid to the temporal performance of the methods

equidistributing principles in moving finite element methods abstract recently miller and his co workers proposed a moving finite element method based on a least squares principle this was followed by a similar method by the present authors using a petrov galerkin approach in this paper the two methods are compared in particular it is shown that both methods move their nodes according to an approximate equidistributing principle this observation leads to a criterion for the placement of the nodes it is also shown that the penalty function designed by miller may also be used with the petrov galerkin method finally numerical examples are given illustrating the performance of the two methods

numerical analysis of elastic plastic rotating disks with arbitrary variable thickness and density abstract a unified numerical method is developed in this article for the analysis of deformations and stresses in elastic plastic rotating disks with arbitrary cross sections of continuously variable thickness and arbitrarily variable density made of nonlinear strain hardening materials the method is based on a polynomial stress plastic strain relation deformation theory in plasticity and von mises yield condition the governing equation is derived from the basic equations of the rotating disks and solved using the runge kutta algorithm the proposed method is applied to calculate the deformations and stresses in various rotating disks these disks include solid disks with constant thickness and constant density annular disks with constant thickness and constant density nonlinearly variable thickness and nonlinearly variable density linearly tapered thickness and linearly variable density and a combined section of continuously variable thickness and constant density the computed results are compared to those obtained from the finite element method and the existing approaches a very good agreement is found between this research and the finite element analysis due to the simplicity effectiveness and efficiency of the proposed method it is especially suitable for the analysis of various rotating disks

moving finite element model for one dimensional infiltration in unsaturated soil the numerical integration of richards equation for infiltration into homogeneous unsaturated soil is carried out by a moving finite element mfe method accurate solution of this one dimensional nonlinear partial differential equation by standard finite difference fd or finite element fe methods can be obtained by using a fine discretization on space and time this can lead to large computer times with the mfe method grid points are moved during computation along the wetting front so that accuracy can be maintained by using a small number of nodes for simulating cases several meters in depth for these cases the mfe method is faster than fd and fe methods the numerical mfe model is verified through comparison with the quasi analytical solution by philip 1957 moreover we compare for some other test problems the computational efficiency of this method with that of two efficient pressure head based fd and fe fixed grid formulations

a finite dimensional realization of the mollifier method for compact operator equations we introduce and analyze a stable procedure for the approximation of f if where f is the least residual norm solution of the minimal norm of the ill posed equation af g with compact operator a x y between hilbert spaces and x has some smoothness assumption our method is based on a finite number of singular values of a and some finite rank operators our results are in a more general setting than the one considered by rieder and schuster 2000 and nair and lal 2003 with special reference to the mollifier method and it is also applicable under fewer smoothness assumptions on

a semi lagrangian approach for american asian options under jump diffusion a semi lagrangian method is presented to price continuously observed fixed strike asian options at each timestep a set of one dimensional partial integrodifferential equations pides is solved and the solution of each pide is updated using semi lagrangian timestepping crank nicolson and second order backward differencing timestepping schemes are studied monotonicity and stability results are derived with low volatility values it is observed that the nonsmoothness at the strike in the payoff affects the convergence rate a subquadratic convergence rate is observed

fourth order finite difference method for solving burgers equation abstract in this paper we present fourth order finite difference method for solving nonlinear one dimensional burgers equation this method is unconditionally stable the convergence analysis of the present method is studied and an upper bound for the error is derived numerical comparisons are made with most of the existing numerical methods for solving this equation

multisymplectic geometry and multisymplectic preissmann scheme for the kdv equation the multisymplectic structure of the kdv equation is presented directly from the variational principle from the numerical view point we give a multisymplectic twelve points scheme which is equivalent to the multisymplectic preissmann scheme finally we test the twelve points scheme on solitary waves over long time intervals

collocation method using quartic b spline for the equal width ew equation the equal width ew equation is solved numerically by giving a new algorithm based on collocation method using quartic b splines at the mid knots points as element shape also we use the fourth runge kutta method for solving the system of first order ordinary differential equations instead of finite difference method our test problems including the migration and interaction of solitary waves are used to validate the algorithm which is found to be accurate and efficient the three invariants of the motion are evaluated to determine the conservation properties of the algorithm the temporal evaluation of a maxwellian initial pulse is then studied

analytical and numerical investigation of strain hardening viscoplastic thick walled cylinders under internal pressure by using sequential limit analysis plastic limit load of strain hardening viscoplastic thick walled cylinders subjected to internal pressure is investigated numerically and analytically in the paper the paper applies sequential limit analysis to deal with the quasi static problem involving hardening material properties and weakening behavior corresponding to the strain rate sensitivity and widening deformation by sequential limit analysis the paper treats the plasticity problems as a sequence of limit analysis problems stated in the upper bound formulation rigorous upper bounds are acquired iteratively through a computational optimization procedure with the internal pressure factor as the objective function especially rigorous validation was conducted by numerical and analytical studies of thick walled cylinders in terms of the plastic limit load as well as the onset of instability it is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions 2007 elsevier b v all rights reserved

a novel numerical scheme for solving burgers equation abstract in this paper we propose a novel numerical scheme for solving burgers equation the scheme is based on a cubic spline quasi interpolant and multi node higher order expansion which make the algorithm simple and easy to implement the numerical experiments show that the proposed method produces high accurate results

moving finite elements i we present new and general numerical methods for dealing with problems whose solutions develop sharp transition layers or near shocks these methods allow many nodes automatically to concentrate in the critical regions and move with them for clarity of exposition we concentrate on the space of piecewise linear functions with movable nodes with burgers equation as our test equation but the generalization to much more general spaces and equations including even certain previous moving vorticity blobs of the first author and s doss for the navier stokes equations becomes clear in this paper we present the theoretical and computational details of our scheme along with computational trial runs for burgers equation showing that the nodes do concentrate sharply and move with the shocks as desired the conclusiveness of these preliminary numerical trials is marred somewhat by the fact that we never successfully debugged a newton s method for our implicit stiff ode solver and were thus limited to ver

elastic stress analysis of rotating converging conical disks subjected to thermal load and having variable density along the radius an analytical procedure for evaluation of elastic stresses and strains in rotating conical disks either solid or annular subjected to thermal load and having a fictitious density variation along the radius is presented the procedure is based on two independent integrals of the hypergeometric differential equation describing the displacement field this procedure is just as general as the one found in technical literature but less intricate and more reliable general unpublished relations of stress state and displacement field in conical disk subjected under elastic conditions to thermal gradient and featuring a density variation along the radius are defined particular consideration is given to some industrial example of turbine rotors carrying hub and rim with buckets on periphery or radial blades on lateral surfaces the analytical results obtained by using the new general relations perfectly match those obtained by fea

investigation of rotating hollow cylinders of strain hardening viscoplastic materials by sequential limit analysis the paper employs sequential limit analysis to investigate rotating hollow cylinders of nonlinear isotropic strain hardening viscoplastic materials a computational optimization procedure was developed to account for hardening material properties and weakening behavior corresponding to the strain rate sensitivity and widening deformation a sequence of limit analysis problems was then conducted to seek the corresponding plastic limit angular velocities sequentially by a general algorithm incorporated with an inner and outer iterative sequence particularly analytical solutions of plastic limit angular velocities and the onset of instability were derived for rigorous comparisons the corresponding stability condition was also obtained explicitly specifically the implicit form of the onset of instability was solved by the fixed point iteration it is found that the computed limit angular velocities are rigorous upper bounds and match well with analytical solutions

numerical solutions of nonlinear burgers equation with modified cubic b splines collocation method abstract in this paper a numerical method is proposed to approximate the solution of the nonlinear burgers equation the method is based on collocation of modified cubic b splines over finite elements so that we have continuity of the dependent variable and its first two derivatives throughout the solution range we apply modified cubic b splines for spatial variable and derivatives which produce a system of first order ordinary differential equations we solve this system by using ssp rk43 or ssp rk54 scheme this method needs less storage space that causes less accumulation of numerical errors the numerical approximate solutions to the burgers equation have been computed without transforming the equation and without using the linearization illustrative eleven examples are included to demonstrate the validity and applicability of the technique easy and economical implementation is the strength of this method

the approximate inverse in action with an application to computerized tomography the approximate inverse is a scheme to obtain stable numerical inversion formulae for linear operator equations of the first kind yet in some applications the computation of a crucial ingredient the reconstruction kernel is time consuming and instable it may even happen that the kernel does not exist for a particular semidiscrete system to cure this dilemma we propose and analyze a technique that is based on a singular value decomposition of the underlying operator the results are applied to the reconstruction problem in 2d computerized tomography where they enable the design of reconstruction filters and lead to a novel error analysis of the filtered backprojection algorithm

higher order accurate numerical solution of unsteady burgers equation abstract higher order accurate finite difference schemes for solving the unsteady burgers equation which often arises in mathematical modeling used to solve problems in fluid dynamics are presented the unsteady burgers equation belongs to a few nonlinear partial differential equations which has an exact solution and it allows one to compare the numerical solution with the exact one and the properties of different numerical methods we propose an explicit finite difference scheme for a numerical solution of the heat equation with robin boundary conditions it has a sixth order approximation in the space variable and a third order approximation in the time variable as an application we developed numerical schemes for solving a numerical solution of burgers equation using the relationship between the heat and burgers equations this scheme has up to sixth order approximation in the space variables the main advantage of our approach is transition to one dimensional equation which essentially reduces the computation costs compared to other direct methods for solving the unsteady burgers equation the numerical results of test examples are found in good agreement with exact solutions for a wide range of reynolds number and confirm the approximation orders of the schemes proposed

convergence analysis and validation of sequential limit analysis of plane strain problems of the von mises model with non linear isotropic hardening the paper presents sequential limit analysis of plane strain problems of the von mises model with non linear isotropic hardening by using a general algorithm the general algorithm is a combined smoothing and successive approximation cssa method in the paper emphasis is placed on its convergence analysis and validation applied to sequential limit analysis involving materials with isotropic hardening by sequential limit analysis the paper treats deforming problems as a sequence of limit analysis problems stated in the upper bound formulation especially the cssa algorithm was proved to be unconditionally convergent by utilizing the cauchy schwarz inequality finally rigorous validation was conducted by numerical and analytical studies of a thick walled cylinder under pressure it is found that the computed limit loads are rigorous upper bounds and agree very well with the analytical solutions copyright 2005 john wiley sons ltd

numerical solutions of the burgers equation by the least squares quadratic b spline finite element method in this study a least squares quadratic b spline finite element method for calculating the numerical solutions of the one dimensional burgers like equations with appropriate boundary and initial conditions is presented three test problems have been studied to demonstrate the accuracy of the present method results obtained by the method have been compared with the exact solution of each problem and are found to be in good agreement with each other a fourier stability analysis of the method is also investigated

a lattice boltzmann model for the generalized burgers huxley equation abstract in this paper we develop a lattice boltzmann model for the generalized burgers huxley equation gbhe by choosing the proper time and space scales and applying the chapman enskog expansion the governing equation is recovered correctly from the lattice boltzmann equation and the local equilibrium distribution functions are obtained excellent agreement with the exact solution is observed and better numerical accuracy is obtained than the available numerical result the results indicate the present model is satisfactory and efficient the method can also be applied to the generalized burgers fisher equation and be extended to multidimensional cases

numerical solution of one dimesional burgers equation explicit and exact explicit finite difference methods this paper presents finite difference solution and analytical solution of the finite difference approximations based on the standard explicit method to the one dimensional burgers equation which arises frequently in the mathematical modelling used to solve problems in fluid dynamics results obtained by these ways for some modest values of viscosity have been compared with the exact fourier one it is shown that they are in good agreement with each other

on generalized ho der inequality inequality may apply to general paired non euclidean norms we restrict the discussion to finite dimensional spaces a theorem is established for such generalized holder inequality together with its sharpness condition the new sharpness condition involves the gradient of the norm function the previous inequalities of this type and their associated sharpness conditions become special cases of this new inequality which is a fundamental primal dual relation of two spaces defined by paired norms on their respective elements given an arbitrarily defined primal norm in one space a method is presented for constructing the dual norm in the other the generalized holder inequality is the basis for many known minimax duality theorems in applied fields particular examples of this duality are found in mathematical models of plastic behavior inequalities appear frequently in algebra geometry and analysis this form of mathematical statements is so prevalent that it is difficult to state their relevance and applications exhaustively inequalities are used to demarcate numbers vectors matrices and functions e g to be positive definite to define sets norm measures convexity of sets and functions to compare and bound functions with another function just to name a few there are books devoted exclusively to inequalities 11 a class of inequalities concerning inner products of vectors and functions can be grouped into two frequently encountered ones in literature although one is a special case of the other the schwarz inequality applies to the euclidean and hilbert spaces 2 the holder inequality extends the concept to certain non euclidean and non hilbert spaces associated with a specific family of norm measures defined by minkowski 3 we shall restrict our discussion to finite dimensional spaces a further extension of the holder inequality is presented in this paper for general paired non euclidean spaces the familiar schwarz inequality for the euclidean space r can be stated for the inner product

moving finite element methods for evolutionary problems ii applications abstract in this the second of two papers on the subject we present applications of the moving finite element method to a number of test problems key features are linear elements a direct approach to parallelism and node overtaking avoiding penalty functions rapid inversion of the mass matrix by preconditioned conjugate gradients and explicit euler time stepping the resulting codes are fast and efficient and are able to follow fronts and similar features with great accuracy the paper includes a substantial section on changes of dependent variable and front tracking techniques for non linear diffusion problems test problems include non linear hyperbolic conservation laws and non linear parabolic equations in one and two dimensions

numerical solution of burgers equation by the sobolev gradient method abstract burgers equation is solved numerically with sobolev gradient methods a comparison is shown with other numerical schemes presented in this journal such as modified adomian method mam 1 and by a variational method vm which is based on the method of discretization in time 2 it is shown that the sobolev gradient methods are highly efficient while at the same time retaining the simplicity of steepest descent algorithms

lattice boltzmann models for two dimensional coupled burgers equations abstract in this paper two lattice boltzmann models for two dimensional coupled burgers equations are proposed through treating the part or all of convection items as the source term where the spatial gradient can be calculated by the distribution function the models can exactly recover the burgers equations without any assumptions some numerical tests are also performed to validate the present models it is found that the proposed models are more accurate and efficient in solving two dimensional coupled burgers equations

a new lattice boltzmann model for solving the coupled viscous burgers equation abstract in this paper a new lattice boltzmann model for the coupled nonlinear system of viscous burgers equation is proposed by using the double evolutionary equations through selecting equilibrium distribution functions and amending functions properly the governing evolution system can be recovered correctly according to our proposed scheme in which the chapman enskog expansion is employed the effects of space and time resolutions on the accuracy and stability of the model are numerically investigated in detail the numerical solutions for various initial and boundary conditions are calculated and validated against analytic solutions or other numerical solutions reported in previous studies it is found that the numerical results agree well with the analytic solutions which indicates the potential of the present algorithm for solving the coupled nonlinear system of viscous burgers equation

unified approach to simulation on deforming elements with application to phase change problems abstract several different approaches to simulation on deforming finite elements are shown to generate the same weighted residuals formulation for the evolution of the dependent variables control of node motion by means of mesh stretching in two dimensions is illustrated in the context of phase change problems simulation of problems with large phase boundary excursions shows good agreement with analytic solutions

stress analysis of functionally graded thick walled cylindrical vessels in this paper a simple and accurate method is presented to determine deformations and stresses in thick walled cylindrical vessels made of functionally graded materials under internal pressure and uniform temperature the governing equation with the consideration of varying young s modulus and thermal expansion coefficient along the radial direction is derived from the basic equations of axisymmetric plane strain problems in elasticity the comparison with the corresponding numerical solution indicates that the proposed solution has excellent convergence and accuracy the effects of the coefficients which affect young s modulus and the thermal expansion coefficient on the deformation and stresses in thick walled cylindrical vessels are investigated

the semidiscrete filtered backprojection algorithm is optimal for tomographic inversion the filtered backprojection algorithm is probably the most often used reconstruction algorithm in two dimensional computerized tomography for a semidiscrete version in the parallel scanning geometry we prove optimal l2 convergence rates for density distributions in sobolev spaces additionally we show l2 convergence without rates when the density distribution is only in l2 the key to success is a new representation of the filtered backprojection which enables us to apply techniques from approximation theory our analysis provides further a modification of the shepp logan reconstruction filter with an improved convergence behavior numerical experiments in the fully discrete setting reproduce the theoretical predictions

a class of high order compact difference schemes for solving the burgers equations abstract in this paper a class of high order compact difference method is introduced for solving the burgers equations firstly a linear high order compact difference scheme is proposed to solve the one dimensional burgers equation the scheme is fourth order accurate in space and second order accurate in time linear stability analysis is conducted to show the scheme is conditionally stable because only three grid points are involved in each time level thomas algorithm can be directly used to solve the tridiagonal linear system then this method is extended to solve the two dimensional and three dimensional coupled burgers equations numerical experiments are carried out to demonstrate the accuracy and dependability of the present method

a numerical solution of the burgers equation using cubic b splines in the present paper numerical solutions of the one dimensional burgers equation are obtained by a method based on collocation of cubic b splines over finite elements the accuracy of the proposed method is demonstrated by three test problems the numerical results are found in good agreement with exact solutions time space integration of the burgers equation yields a system of difference equation which is shown to be unconditionally stable

local rbf method for multi dimensional partial differential equations abstract in this paper a local meshless differential quadrature collocation method is utilized to solve multi dimensional reaction convection diffusion pdes numerically in some cases global version of the meshless method is considered as well the meshless methods approximate solution on scattered and uniform nodes in both local and global sense in the case of convection dominated pdes the local meshless method is coupled with an upwind technique to avoid spurious oscillations for this purpose a physically motivated local domain is utilized in the flow direction both regular and irregular geometries are taken into consideration numerical experiments are performed to demonstrate effective applications and accuracy of the meshless method on regular and irregular domains

large deformation of structures by sequential limit analysis although most structures are designed to function under small deformation their large deformation behavior can be used to estimate reliability and safety for survivorship from an accident or a natural disaster structures such as buildings bridges ships vehicles and machinery are designed with a safety factor to protect certain assets from the unexpected and unknot elements the large deformation analysis provides the rational basis for a safety factor in this paper the method of sequential limit analysis is used to compute large deformation solutions of truss and frame problems differing from the incremental method of plasticity the limit analysis method is numerically stable more effecient and requires simpler input data a duality theorem serves as the foundation of an algorithm for computing the complete static and kinematic solutions sim uhaneously and for establishing their accuracy in each step of a deformation sequence the phenom ena encountered in large deformation such as loading unloading under monotone deformation bifurcation more generally loss of uniqueness of solutions and internal contact of structural members are revealed by the sequential limit analysis presented in this paper

an mpec approach for the critical post collapse behavior of rigid plastic structures this paper presents a numerical method to identify and trace the critical post collapse response of rigid perfectly plastic structures to account for the possibility of multiple equilibrium paths the critical one is directly identified using the minimum 2nd order work criterion our proposed enhanced sequential limit analysis is formulated as an instance of the challenging class of optimization problems known as a mathematical program with equilibrium constraints mpec this mpec formulation minimizes the 2nd order work expression subject to the set of constraints describing the complete complementarity system in mixed static kinematic variables governing simultaneously the two adjacent equilibrium configurations namely the current one and its neighboring state we use a nonlinear programming based algorithm involving relaxation of the complementarity terms to solve the mpec four numerical examples are provided to illustrate application of the proposed scheme

numerical solution of the burgers equation by automatic differentiation abstract we compute the solution of the one dimensional burgers equation by marching the solution in time using a taylor series expansion our approach does not require symbolic manipulation and does not involve the solution of a system of linear or non linear algebraic equations instead we use recursive formulas obtained from the differential equation to calculate exact values of the derivatives needed in the taylor series we illustrate the effectiveness of our method by solving four test problems with known exact solutions the numerical solutions we obtain are in excellent agreement with the exact solutions while being superior to other previously reported numerical solutions

a numerical method based on crank nicolson scheme for burgers equation abstract in this paper we present a solution based on crank nicolson finite difference method for one dimensional burgers equation burgers equation arises frequently in mathematical modeling of problems in fluid dynamics hopf cole transformation e hopf the partial differential equation u t uu x u xx commun pure appl math 3 1950 201 230 j d cole on a quasilinear parabolic equation occurring in aerodynamics quart appl math 9 1951 225 236 is used to linearize burgers equation the resulting heat equation is discretized by using crank nicolson finite difference scheme this method is shown to be unconditionally stable and second order accurate in space and time numerical results obtained by the present method have been compared with exact solution for different values of reynolds number

an implementation of a moving finite element method abstract the moving finite element method an adaptive gridding procedure for systems of partial differential equations whose solutions contain steep gradients has been implemented in a very straightforward way accurate results can be obtained using fewer nodes than that required by fixed mesh solution methods performance of the method using some minor changes to a standard ordinary differential equation algorithm is illustrated with solutions to burger s equation

elastic stress analysis of non linear variable thickness rotating disks subjected to thermal load and having variable density along the radius an analytical procedure for evaluation of elastic stresses and strains in non linear variable thickness rotating disks either solid or annular subjected to thermal load and having a fictitious density variation along the radius is presented thickness variation of disks is described by means of a power of linear function which can be used to describe a fourfold infinity of actual disk profiles the procedure is based on two independent integrals of the hypergeometric differential equation describing the displacement field this theoretical procedure is just general and does not present limitations and drawbacks of the approaches as the one found in technical literature general unpublished relations of stress state and displacement field in non linear variable thickness disks subjected under elastic conditions to thermal gradient and featuring a density variation along the radius are defined particular consideration is given to some industrial example of turbine rotors carrying hub and rim with buckets on periphery or radial blades on lateral surfaces the analytical results obtained by using the new general relations perfectly match those obtained by fea and overlap those concerning the special cases of tapered conical disks found in literature

a space time fully decoupled wavelet galerkin method for solving two dimensional burgers equations abstract a space time fully decoupled formulation for solving two dimensional burgers equations is proposed based on the coiflet type wavelet sampling approximation for a function defined on a bounded interval by applying a wavelet galerkin approach for spatial discretization nonlinear partial differential equations are first transformed into a system of ordinary differential equations in which all matrices are completely independent of time and never need to be updated in the time integration finally the mixed explicit implicit scheme is employed to solve the resulting semi discretization system by numerically studying three widely considered test problems results demonstrate that the proposed method has a much better accuracy and a faster convergence rate than many existing numerical methods most importantly the study also indicates that the present wavelet method is capable of solving the two dimensional burgers equation at high reynolds numbers

stable lattice boltzmann schemes with a dual entropy approach for monodimensional nonlinear waves we follow the mathematical framework proposed by bouchut 2003 22 and present in this contribution a dual entropy approach for determining equilibrium states of a lattice boltzmann scheme this method is expressed in terms of the dual of the mathematical entropy relative to the underlying conservation law it appears as a good mathematical framework for establishing a h theorem for the system of equations with discrete velocities the dual entropy approach is used with d1q3 lattice boltzmann schemes for the burgers equation it conducts to the explicitation of three different equilibrium distributions of particles and induces naturally a nonlinear stability condition satisfactory numerical results for strong nonlinear shocks and rarefactions are presented we prove also that the dual entropy approach can be applied with a d1q3 lattice boltzmann scheme for systems of linear and nonlinear acoustics and we present a numerical result with strong nonlinear waves for nonlinear acoustics we establish also a negative result with the present framework the dual entropy approach cannot be used for the shallow water equations

the moving finite element method applications to general partial differential equations with multiple large gradients abstract the moving finite element mfe method has been reduced to practice in the automatic solution program dyla for general systems of transient partial differential equations pdes in 1 d several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the mfe method computational dilemmas of numerical diffusion gibbs overshooting and undershooting zone tangling and grid remap or re connection aliasing which occur frequently in conventional pde methods are essentially eliminated in the mfe method arbitrarily large gradients or shocks can be solved with extremely high resolution and accuracy for non coincident or even counterdirected propagating wavefronts boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large scale structures in reactive and non reactive fluid calculations the mfe method requires a small fraction of the grid nodes which are used in conventional pde solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate pde solutions on entire problem domains courant friedrichs lewy time step limits are exceeded by wide margins by factors of two to several thousand finally the extension of the mfe method to 2 d is briefly discussed

weighted finite difference techniques for the one dimensional advection diffusion equation various numerical techniques will be developed and compared for solving the one dimensional advection diffusion equation with constant coefficient these techniques are based on the two level finite difference approximations the basis of analysis of the finite difference equations considered here is the modified equivalent partial differential equation approach developed from the 1974 work of warming and hyett this allows direct and simple comparison of the errors associated with the equations as well as providing a means to develop more accurate finite difference schemes the new methods are more accurate and are more efficient than the conventional techniques these schemes are free of numerical diffusion the results of a numerical experiment are presented and the accuracy and central processor cpu time needed are discussed and compared

some implicit methods for the numerical solution of burgers equation in this article we develop multisymplectic box methods on burgers equation burgers equation has some discontinuous solutions because of effects of viscosity term these discontinuities raise phenomenon of shock waves some explicit and implicit numerical methods have been experimented on burgers equation but these schemes have not been seen proper in this case because of their conditional stability and existence of viscosity term to avoid these problems multisymplectic box scheme which has been constructed for kdv equation is purposed for burgers equation multisymplectic box scheme is a very effective box scheme in diminishing artificial wiggles which appear in approximation solutions we consider two types of box schemes and implement on burgers equation to get better results with no artificial wiggles

2n order compact finite difference scheme with collocation method for solving the generalized burger s huxley and burger s fisher equations the generalized burger s huxley and burger s fisher equations are solved by fully different numerical scheme the equations are discretized in time by a new linear approximation scheme and in space by 2n order compact finite difference scheme after that a collocation method is applied also the two dimensional unsteady burger s equation is described by our proposed scheme numerical experiments and numerical comparisons are presented to show the efficiency and the accuracy of the proposed scheme

lattice boltzmann method for one and two dimensional burgers equation abstract in this paper a new method higher order moment lattice boltzmann method for one and two dimensional burgers equation is proposed the lattice boltzmann models presented here are based on a series of lattice boltzmann equations in different time scales in order to achieve higher order accuracy we use seven and four moments of the equilibrium distribution function in one and two dimensional models respectively we find two kinds of strategy to seek equilibrium distribution functions for the two dimensional model with second order accuracy these two are equivalent when a scale factor k 2 3 lastly we provide a fine numerical result of a one dimensional burgers equation numerical examples show the method can be used to simulate one and two dimensional burgers equation

the approximate inverse in action iii 3d doppler tomography the approximate inverse is a powerful tool for solving first kind operator equations in a stable way its abstract convergence and stability theory developed in our articles siam j numer anal 37 1909 1929 2000 and math comp 72 1399 1415 2003 is applied to the reconstruction problem of 3d vector field tomography resulting in a reconstruction algorithm of filtered backprojection type for an analytically computed reconstruction filter reconstruction kernel convergence with rates as well as the regularization property are established

the modified local crank nicolson method for one and two dimensional burgers equations the modified local crank nicolson method is applied to solve one and two dimensional burgers equations new difference schemes that are explicit unconditionally stable and easy to compute are obtained numerical solutions obtained by the present method are compared with exact solutions and it is seen that they are in excellent agreement

numerical solution of burgers equation by cubic hermite collocation method abstract in this paper numerical solution of the non linear burgers equation are obtained by using cubic hermite collocation method chcm the advantage of the method is continuity of the dependent variable and its derivative throughout the solution range a linear stability analysis shows that the numerical scheme based on crank nicolson approximation in time is unconditionally stable this method is applied on some test problems with different choice of collocation points to validate the accuracy of the method the obtained numerical results show that the method is efficient robust and reliable even for high reynolds numbers for which the exact solution fails moreover the method can be applied to a wide class of nonlinear partial differential equations

a novel lattice boltzmann model for the coupled viscous burgers equations abstract in this work a new lattice boltzmann model for coupled burgers equations is proposed through selecting proper distribution functions unlike the previous models the present model can exactly recover the coupled equations without any assumptions a detailed numerical study on several coupled burgers equations is performed to validate the present model and the results show that the present model not only has a second order convergence rate in space but also is more accurate than the previous model