numerical solutions of the modified burgers equation by petrov galerkin method abstract the modified burgers equation mbe is solved numerically by the petrov galerkin method using a linear hat function as the trial function and a cubic b spline function as the test function product approximation has been used in this method a linear stability analysis of the scheme shows it to be unconditionally stable the accuracy of the presented method is demonstrated by two test problems the numerical results are found in good agreement with the exact solutions

cohomological degrees and hilbert functions of graded modules making use of the recent construction of cohomological degrees functions we give several estimates on the relationship between number of generators and degrees of ideals and modules with applications to hilbert functions they extend results heretofore known from generalized cohen macaulay local rings to nearly arbitrary local rings the rules of computation these functions satisfy enables comparison with castelnuovo mumford s regularity in the graded case as application we derive sharp improvements on predicting the outcome of effecting noether normalizations in tangent cones

normalization of modules we introduce techniques to derive estimates for the degrees of the generators of the integral closure of several classes of rees algebras of modules and to bound the length of normalization processes in the case of regular base rings the bounds are expressed in terms of buchsbaum rim multiplicities and a module version of briancon skoda numbers

variational multiscale element free galerkin method for 2d burgers equation a new numerical method which is based on the coupling between variational multiscale method and meshfree methods is developed for 2d burgers equation with various values of re the proposed method takes full advantage of meshfree methods therefore no mesh generation and mesh recreation are involved meanwhile compared with the variational multiscale finite element method a strong assumption that is the fine scale vanishes identically over the element boundaries although non zero within the elements is not needed subsequently two problems which have an available analytical solution of their own are solved to analyze the convergence behaviour of the proposed method finally a 2d burgers equation having large re is solved and the results have also been compared with the ones computed by two other methods the numerical results show that the proposed method can indeed obtain accurate numerical results for 2d burgers equation having large re which does not refer to the choice of a proper stabilization parameter

numerical approach for solving diffusion problems using cubic b spline collocation method abstract a numerical approach for modeling the removal of homogeneous solutes from the porous structure is presented pore diffusion equations controlling the overall process are expressed in terms of concentration of solute as a function of position in bed and washing period a computational scheme specifying knot vector s and control points de boor points to solve diffusion model using cubic b spline collocation method cscm is given the knot vector provides sufficient resolution and control points yield an accurate approximation of the desired curve convergence of numerical scheme is of o h 2 four problems have been worked out by the proposed scheme results are plotted graphically for fairly wide range of parameters a comparison with the previous techniques demonstrates the superiority of the proposed method on basis of computational time efficiency and accuracy

numerical solution of burgers equation by lattice boltzmann method in this paper a lattice boltzmann model for burgers equation is proposed through selecting equilibrium distribution function properly the model has been verified by three test examples the numerical results are found in good agreement with analytical solutions and numerical solutions reported in previous studies the advantages of the resulting method are algorithmic simplicity parallel computation easy handling of complicated boundary conditions so it is very easy to implement and deal with more complex problems

combination tones in the response of single degree of freedom systems with quadratic and cubic non linearities abstract the method of multiple scales is used to analyze the response of a single degree of freedom system to either the combination resonance of the additive type 2 1 0 or the combination resonance of the difference type 2 1 0 where 1 and 2 are the frequencies of the excitation and 0 is the linear undamped natural frequency of the system to the second approximation the combination resonance of the additive type has three effects on the steady state response first it produces terms having the frequencies 1 2 and 2 1 at first order and terms having the frequencies 0 2 1 2 2 2 1 2 2 1 2 2 1 and 2 2 1 at second order second it produces a shift in the natural frequency of the system third it produces a virtual primary resonant excitation having the frequency 2 1 0 that makes the component having the frequency 2 1 be of first rather than second order similar effects are produced by a combination resonance of the difference type or a superharmonic resonance of order two

combination resonances in the non linear response of bowed structures to a harmonic excitation a second order uniform expansion is obtained for the response of a bowed structure systems with quadratic and cubic non linearities to a combination resonance the results show that combination resonances of the difference type can never be excited moreover the results show that the steady state amplitudes depend strongly on the second mode excitation amplitude f2 two threshold values 1 and 2 for f2 are identified when f2 2 combination resonances are always excited and when 2 f2 2 combination resonances may or may not be excited depending on the initial conditions the results also show that combination resonances are very sensitive to the addition of a first mode excitation amplitude f1 for a certain range of values of f1f2 and the phase angle between the two excitations combination resonances are quenched and the response consistes essentially of the linear response the quenching of combination resonances has been verified by numerically integrating the original differential equations in the presence as well as the absence of internal resonances the analysis also identifies a range of values of f1f2 and for which the response is significantly enhanced this result has also been verified by numerically integrating the original equations in the presence as well as the absence of internal resonances

asymptotic prime divisors of torsion free symmetric powers of modules let r be a noetherian ring f rr and m f a submodule of rank r let a m denote the stable value of ass fn mn for n large where fn is the nth symmetric power of fn and mn is the image of the nth symmetric power of m in fn we provide a number of characterizations for a prime ideal to belong to a m we also show that a m a m where a m denotes the stable value of ass fn mn

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

a geometric theory of the buchsbaum rim multiplicity abstract we develop a self contained theory of a generalized buchsbaum rim multiplicity based on elementary abstract algebraic geometry we define the multiplicity as the sum of certain natural intersection numbers and recover the traditional definition in terms of the leading coefficient of the polynomial that gives the appropriate lengths we interpret the partial sums as the multiplicities in certain closely associated cases we prove an additivity formula in the rings and relate constancy to a generalized notion of reductions we establish a polar multiplicity formula and a mixed multiplicity formula and we determine when each of the four types of multiplicities vanish we end by generalizing the height inequality for maximal minors and a celebrated theorem of boger

variational iteration method for solving burger s and coupled burger s equations by means of variational iteration method the solutions of burger s equation and coupled burger s equations are exactly obtained comparison with the adomian decomposition method is made showing that the former is more effective than the later in this paper he s variational iteration method is introduced to overcome the difficulty arising in calculating adomian polynomials

biorthogonal multiwavelets on the interval for numerical solutions of burgers equation to numerically solve the burgers equation in this paper we propose a general method for constructing wavelet bases on the interval 0 1 derived from symmetric biorthogonal multiwavelets on the real line in particular we obtain wavelet bases with simple structures on the interval 0 1 from the hermite cubic splines in comparison with all other known constructed wavelets on the interval 0 1 our constructed wavelet bases on the interval 0 1 from the hermite cubic splines not only have good approximation and symmetry properties with extremely short supports but also employ a minimum number of boundary wavelets with a very simple structure these desirable properties make them to be of particular interest in numerical algorithms our constructed wavelet bases on the interval 0 1 are then used to solve the nonlinear burgers equation our method is based on the finite difference formula combined with the collocation method therefore our proposed numerical scheme in this paper is abbreviated as mfdcm mixed finite difference and collocation method some numerical examples are provided to demonstrate the validity and applicability of our proposed method which can be easily implemented to produce a desired accuracy

response of self excited two degree of freedom systems to multifrequency excitations the response to multifrequency excitation of a two degree of freedom self excited system is analyzed by using the method of multiple scales three cases of resonance are considered superharmonic primary and subharmonic also considered is the case of simultaneous superharmonic and subharmonic resonance steady state and stability analyses are carried out for each case and numerical results are presented showing the influences of the several parameters

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

a direct variational methods applied to burgers equation in this study a compact approximate method in limiting form for calculating the solution of burgers equation with appropriate boundary conditions is presented the results obtained by present method are found to be in good agreement with those due to earlier authors and offers appreciable advantages for burgers like nonlinear problems

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

on a problem of modified lindstedt poincare for certain strongly non linear oscillators in the present paper concerns the modified lindstedt poincare method is presented for extending the rang of the validity of perturbation expansion to strongly non linear oscillation it is an effective method for dealing with strongly non linear vibration of single degree of freedom system which cannot be treated by the standard l p method therefore a strongly non linear system with large parameter m is transformed into a small parameter system with respect to a this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically this method is suitable for the system with even non linearities as well as with odd non linearities all numerical results computed are in pretty good and displayed graphysically

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

numerical solution of nonlinear burgers equation using high accuracy multi quadric quasi interpolation in this paper a numerical method is presented to approximate the solution to nonlinear burgers equation which is related to many scientific research topics a numerical scheme by using high accuracy multi quadric quasi interpolation is presented in which a kind of multi quadric quasi interpolant is used to approximate the derivatives of the solution in spatial domain and finite difference is used to approximate the derivatives of the solution in temporal domain the advantage of the scheme is that it is mesh free and in each time step only a multi quadric quasi interpolant is employed so that the algorithm is easy to implement the numerical results of this scheme are also shown and compared with other numerical schemes

parametrically excited non linear systems a comparison of two methods subharmonic resonance of two degree of freedom systems with cubic non linearities to multifrequency parametric excitations in the presence of three to one internal resonance is investigated two approximate methods the multiple scales and the generalized synchronization are used to construct first order non linear ordinary differential equations governing the modulation of the amplitudes and phases steady state solutions and their stability are computed for selected values of the system parameters the results obtained by the two methods are in excellent agreement numerical solutions are carried out and graphical representations of the results are presented and discussed

appropriate stabilized galerkin approaches for solving two dimensional coupled burgers equations at high reynolds numbers abstract this paper aims to seek proper stabilized galerkin methods for solving the two dimensional coupled burgers equations at high reynolds numbers the stabilization techniques employed here include the streamline upwind petrov galerkin supg method the spurious oscillations at layers diminishing sold method and the characteristic galerkin cg method the first two methods are combined with the crank nicolson scheme for time discretization and the last one is applied in its semi implicit version different from most of the studies on the equations which are usually devoted to improving the accuracy of computed solution in the case of low reynolds numbers this paper mainly focuses on keeping the stability of the solution at high reynolds numbers which is significant in practical applications and also challenging in numerical computation we study two problems equipped with mixed boundary conditions and only dirichlet boundary conditions respectively numerical experiments reveal that the supg method is optimal for the former problem and the sold method is more appropriate for the latter one in addition the performances of these methods demonstrate the difference between the two problems which is seldom mentioned previously and might be helpful to other conventional methods intending to solve the problems at high reynolds numbers and last since sold methods have rarely been utilized to solve nonlinear unsteady problems before this study also indicates the potential of this class of methods to solve nonlinear unsteady convection dominated problems

the generalized boundary element approach to burgers equation the generalized boundary element method is presented for the numerical solution of burgers equation the new method is based on the set of boundary integral equations derived for each subdomain by using the fundamental solution for the linearized differential operator of the equation the resulting system of quasi non linear equations is solved implicitly with use of a simple iterative procedure the adaptability and the accuracy of the proposed method are demonstrated by three examples and a comparison of the numerical results with the exact solution or other existing solutions is shown for the first example

length formulas for the local cohomology of exterior powers in 10 huneke noted a proof due to hochster of the following theorem of angeniol and giusti see 1 let r be a local ring n m and g r r a homomorphism such that grade im g n m l suppose the cokernel n of g has finite length then this length equals the length of r ira g n 2 r ira g by i g we denote the ideal in r generated by the m x m minors of a matrix representing g it is well known see 7 that n m 1 is the maximal possible grade if im g t r therefore r is a cohen macaulay ring of dimension n m 1 we further notice that angeniol and giusti in addition assume r to contain the rational numbers and that the theorem has been known for a long time if m n 9 21 10 17 2 in this paper we shall study the problem of angeniol and giusti in a more general context we start from the dual situation f rm r being a homomorphism which we assume to be injective this is equivalent to grade ira f 1 given a basis x of r m and an orientation 7 on r i e an

a galerkin finite element approach to burgers equation a galerkin finite element method is presented for the numerical solution of burgers equation a linear recurrence relationship for the numerical solution of the resulting system of ordinary differential equations is found via a crank nicolson approach involving a product approximation it is shown that this method is capable of solving burgers equation accurately for a wide range of viscosity values the results show that the new method performs better than the most of the methods available in the literature

on the buchsbaum rim function of a parameter module abstract in this article we prove that the buchsbaum rim function l a s 1 f n 1 of a parameter module n in f is bounded above by e f n d r 1 d r 1 for every integer 0 moreover it turns out that the base ring a is cohen macaulay once the equality holds for some integer as a direct consequence we observe that the first buchsbaum rim coefficient e 1 f n of a parameter module n is always non positive

the buchsbaum rim polynomial of a module abstract for a noetherian local ring r m the hilbert functions of m primary ideals provide considerable information about constructions and singularities coded by the ideal for a module e which is the analogue of such ideals e is a proper submodule of a free module so that the quotient has finite length buchsbaum and rim defined a similar function and introduced the notion of buchsbaum rim multiplicity br e of the module unlike in the ideal case the information about these functions is still scant when r is cohen macaulay of dimension d 1 and e has rank r we develop some of their properties sufficiently enough to establish the following bound for the reduction number of the module e r e d r 1 br e 2 1 the same techniques lead to bounds on the number of generators of the integral closure of the powers of certain ideals and modules

effective normality criteria for algebras of linear type abstract the algebras studied here are subalgebras of rings of polynomials generated by 1 forms so called rees algebras with coefficients in a noetherian ring given a normal domain r and a torsionfree module e with a free resolution f 2 f 1 f 0 e 0 we study the role of the matrices of syzygies in the normality of the rees algebra of e when the rees algebra r e and the symmetric algebra s e coincide the main results characterize normality in terms of the ideal ic s e and of the completeness of the first s symmetric powers of e where c rank and s rankf0 ranke it requires that r be a regular domain special results under broader conditions on r are still more effective

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

an exponentially fitted method for solving burgers equation in this paper an exponentially fitted method is used to numerically solve the one dimensional burgers equation the performance of the method is tested on the model involving moderately large reynolds numbers the obtained numerical results show that the method is efficient stable and reliable for solving burgers equation accurately even involving high reynolds numbers for which the exact solution fails copyright 2009 john wiley sons ltd

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

b spline galerkin methods for numerical solutions of the burgers equation the first order splitting method is applied to the burgers equation and two numerical algorithms are set up for this time splitted burgers equation using both quadratic and cubic b spline galerkin finite element techniques the unknowns in the equation is resolved with the b splines in space and standart crank nicolson differencing schemes is used to advance solution in time results of three numerical test problems are used to compare each schemes with available some results

an algorithm based on exponential modified cubic b spline differential quadrature method for nonlinear burgers equation in this paper the authors developed a new differential quadrature method exponential modified cubic b spline differential quadrature method expo mcb dqm by using exponential modified cubic b spline functions as test functions in the traditional differential quadrature method 32 the new method is tested on one and two dimensional nonlinear burgers equations to check the efficiency and accuracy of the proposed method five numerical problems have been considered the numerical results of the method are compared with some existing methods and found that the proposed numerical method produces more accurate results than existing methods stability analysis of the algorithm is also done by using matrix stability analysis method

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

symmetric powers of complete modules over a two dimensional regular local ring this is the published version also available here http dx doi org 10 1090 s0002 9947 97 01819 9 first published in trans amer math soc in 1997 published by the american mathematical society

dynamics in spectral solutions of burgers equation for low values of the viscosity coefficient burgers equation can develop sharp discontinuities which are difficult to simulate in a computer oscillations can occur by discretization through spectral collocation methods due to gibbs phenomena under a dynamic point of view these instabilities are related to bifurcations arising to the discretized equation for different values of discretized points herein a study is performed of the dynamics and bifurcations occurring in the spectral solutions of burgers equation with symmetry several phenomena are observed from limit cycles strange attractors to the presence of bistability with two periodic attractors with a periodic attractor and a strange attractor and with two strange attractors also other stable equilibrium points can occur diverse from the ones corresponding to the solution of burgers equation

a new low order least squares nonconforming characteristics mixed finite element method for burgers equation in this paper a new low order least squares nonconforming characteristics mixed finite element method mfem is considered for two dimensional burgers equation by use of two typical characters of the elements for approximating the velocity and flux variables a the consistency errors of the elements can be estimated as order o h 2 with respect to the mesh size h in the broken h 1 norm one order higher than their interpolation errors b the elements interpolation operators satisfy certain orthogonalities which lead to o h 2 order error estimates in l 2 norm and some superclose results the accuracy of corresponding variables in l 2 norm is improved by one order compared with other mfems in the existing literature it seems that the results provided herein have never been derived before