a rbf based differential quadrature method for solving two dimensional variable order time fractional advection diffusion equation abstract numerical simulation technique of two dimensional variable order time fractional advection diffusion equation is developed in this paper using radial basis function based differential quadrature method rbf dq to the best of the authors knowledge this is the first application of this method to variable order time fractional advection diffusion equations for the general case of irregular geometries the meshless local form of rbf dq is used and the multiquadric type of radial basis functions is selected for the computations this approach allows one to define a reconstruction of the local radial basis functions to treat accurately both the dirichlet and neumann boundary conditions on the irregular boundaries the method is validated by the well documented test examples involving variable order fractional modeling of air pollution the numerical results demonstrate that the proposed method provides accurate solutions for two dimensional variable order time fractional advection diffusion equations

operations on fuzzy ideals in this paper we give suitable definitions of the operations of l fuzzy ideals in a ring as intersection addition multiplication and residual division and we prove some fundamental properties of the operations analogous to those that hold for the operations of ordinary ideals see 3

implementation of a variable stepsize variable formula method in the time integration part of a code for treatment of long range transport of air pollutants abstract a mathematical model consisting of two partial differential equations is used to study the long range transport of sulphur di oxide and sulphate over europe the discretization of the first order space derivatives the advection terms is carried out by a pseudospectral fourier algorithm a special technique is applied in the discretization of the second order space derivatives the diffusion terms two large systems of ordinary differential equations are solved at each time step it is shown that these systems can efficiently be treated by a variable stepsize variable formula method vsvfm based on the use of predictor corrector schemes the stepsize selection strategy and the formula selection strategy are discussed in detail an attempt to carry out both an accuracy control and a stability control is made at each time step the great efficiency of the vsvfm implemented in our software as well as the reliability of the results are illustrated by numerical experiments in which real meteorological data for 1979 at the grid points of a space domain covering the whole of europe were used the main ideas implemented in the time integration part might be applied in many other situations where the systems of ordinary differential equations arising after the space discretization are only moderately stiff so that the stability requirements are dominant over the accuracy requirements on a large part of the time interval but the use of implicit time integration algorithms that require solving systems of algebraic equations at each time step is not justified as an illustration only it should be mentioned that such an application has been carried out in connection with models describing long range transport of nitrogen pollutants over europe

taylor series approach for function approximation using estimated higher derivatives the paper proposes a new approach for function approximation by estimating the second derivative using taylor series where the samples of the function and its first derivatives at the sample points are known without such estimation these initial data can approximate the function traditionally using the first order taylor approximation but with more error if we desire to improve the approximation via second order taylor series then we can estimate the pseudo second derivatives of the function in three different ways all these three ways are investigated in this paper the pseudo second derivatives help in computing many more sample points of the function within each sampling interval thus the approach acts like a mathematical magnifying glass two examples are treated to compare the efficiencies of the methods also a qualitative study for upper bound of error of the approximations is studied in detail

a high order exponential scheme for solving 1d unsteady convection diffusion equations in this paper a high order exponential hoe scheme is developed for the solution of the unsteady one dimensional convection diffusion equation the present scheme uses the fourth order compact exponential difference formula for the spatial discretization and the 2 2 pade approximation for the temporal discretization the proposed scheme achieves fourth order accuracy in temporal and spatial variables and is unconditionally stable numerical experiments are carried out to demonstrate its accuracy and to compare it with analytic solutions and numerical results established by other methods in the literature the results show that the present scheme gives highly accurate solutions for all test examples and can get excellent solutions for convection dominated problems

fuzzy primary representations of fuzzy ideals abstract let r be a commutative ring with identity and let a be a fuzzy ideal of r then a is said to have a fuzzy primary representation if a is the intersection of a finite number of fuzzy primary ideals we show that every fuzzy ideal a of r such that a 0 1 has a fuzzy primary representation if and only if r is artinian we show that uniqueness properties for reduced primary representations of ideals in the usual sense carry over to fuzzy ideals

a high order scheme for unsteady heat conduction equations abstract in this work a high order scheme is proposed for solving the heat conduction problems in this scheme the governing equation of heat conduction is firstly written into a system of first order partial differential equations which are integrated over the control volumes around each node point and a finite time step the resulting time integrals are approximated by numerical quadrature with an undetermined weighting parameter the error analysis allows us to determine the parameter and the ratio of the time step to the square of grid spacing by making the error of the scheme as small as possible both theoretical and numerical results show that the proposed high order scheme can achieve at least sixth order accuracy at the expense of the same computing cost as the traditional finite volume method and the high order scheme demonstrates a better performance than the high order compact finite difference method and the runge kutta discontinuous galerkin method

some results on l fuzzy modules abstract an l fuzzy quotient module of a module is redefined and a modular complete pseudo complemented lattice structure is given to the set of all l fuzzy modules of a given module some isomorphisms between the lattices or posets of l fuzzy modules are obtained finally a galois connection is established between two lattices of l fuzzy modules of homomorphic modules

simple accurate and efficient revisions to maccormack and saulyev schemes high peclet numbers abstract stream water quality modeling often involves numerical methods to solve the dynamic one dimensional advection dispersion reaction equations adre there are numerous explicit and implicit finite difference schemes for solving these problems and two commonly used schemes are the maccormack and saulyev schemes this paper presents simple revisions to these schemes that make them more accurate without significant loss of computation efficiency using advection dominated high peclet number problems as test cases performances of the revised schemes are compared to performances of five classic schemes forward time centered space ftcs backward time centered space btcs crank nicolson and the traditional maccormack and saulyev schemes all seven of the above numerical schemes were tested against analytical solutions for pulse and step inputs of mass to a steady flow in a channel and performances were considered with respect to stability accuracy and computational efficiency results indicated that both the modified saulyev and the maccormack schemes which are named the saulyevc and maccormackc schemes respectively greatly improved the prediction accuracy over the original ones the computation efficiency in terms of cpu time was not impacted for the saulyevc scheme the maccormackc scheme demonstrated increased time consumption but was still much faster than implicit schemes

iterative solvers for a spectral galerkin approach to elliptic partial differential equations with fuzzy coefficients mathematical models of physical systems often contain parameters with an imprecisely known and uncertain character it is quite common to represent these parameters by means of random variables numerous methods have been developed to compute accurate approximations to solutions of equations with such parameters this approach however may not be entirely justified when the uncertainty is due to vagueness or incomplete knowledge for such cases alternative uncertainty representations using tools from imprecise probability theory have been suggested among those the fuzzy representation is probably most popular in this paper we consider numerical methods for solving partial differential equations with fuzzy coefficients we demonstrate that spectral expansion methods quite common in the random variable approach can also be used effectively for solving fuzzy equations we motivate the use of chebyshev polynomials in the spectral representation and apply a galerkin projection to convert the fuzzy prob

the use of proper orthogonal decomposition pod meshless rbf fd technique to simulate the shallow water equations abstract the main aim of this paper is to develop a fast and efficient local meshless method for solving shallow water equations in one and two dimensional cases the mentioned equation has been classified in category of advection equations the solutions of advection equations have some shock thus especial numerical methods should be employed for example discontinuous galerkin and finite volume methods here based on the proper orthogonal decomposition approach we want to construct a fast meshless method to this end we consider shallow water models and obtain a suitable time discrete scheme based on the predictor corrector technique then by applying the proper orthogonal decomposition technique a new set of basis functions can be built for the solution space in which the size of new solution space is less than the original problem thus by employing the new bases the cpu time will be reduced some examples have been studied to show the efficiency of the present numerical technique

accurate discretization of advection diffusion equations we present an exact mathematical transformation which converts a wide class of advection diffusion equations into a form allowing simple and direct spatial discretization in all dimensions and thus the construction of accurate and more efficient numerical algorithms these discretized forms can also be viewed as master equations which provide an alternative mesoscopic interpretation of advection diffusion processes in terms of diffusion with spatially varying hopping rates

galerkin least square b spline approach toward advection diffusion equation the study uses weighted residual least squares method using cubic b splines a numerical scheme is developed to solve pdes involving advection diffusion type phenomenon the validity of the scheme is tested with several model problems method is shown to be highly accurate and computationally efficient stability and error analysis are presented advection diffusion equation is one of the governing equations used for modeling solute transport processes and water quality in rivers lakes oceans and groundwater etc to simulate this class of mathematical problems a computational scheme based on weighted residual least squares method using cubic b splines is developed in this paper moreover some test cases and results obtained are discussed and compared with the available data the suggested method is shown to be accurate enough through these test examples

an optimal time stepping algorithm for unsteady advection diffusion problems we consider the numerical solution of a linear time dependent advection diffusion problem by an implicit two weight three point finite difference scheme we extend the scheme proposed by chadha and madden 2011 to incorporate an optimal time step selection algorithm for the method the optimal values of the weights involved in the scheme have been obtained by using the notion of an equivalent differential equation warming and hyett 1974 and by enforcing certain constraints due to von neumann stability and a discrete maximum principle we obtain sharp bounds for optimal time stepping in terms of mesh width and problem data furthermore we formulate the time step selection as a root finding problem and use this to show the optimal time step exists and is unique the resulting method based on optimal values of weights and optimal time stepping is of fifth order in space and third order in time the results of extensive numerical experiments are presented for several classic test problems for various values of the advection and diffusion parameters these show that our proposed method is superior quantitatively and qualitatively to other schemes that can be represented within the framework of two weighted schemes we also present comparisons with other high order methods and an application of the method to a problem with non smooth data

numerical solution of unsteady advection dispersion equation arising in contaminant transport through porous media using neural networks a soft computing approach based on artificial neural network ann and optimization is presented for the numerical solution of the unsteady one dimensional advection dispersion equation ade arising in contaminant transport through porous media a length factor ann method based on automatic satisfaction of arbitrary boundary conditions bcs was chosen for the numerical solution of ade the strength of ann is exploited to construct a trial approximate solution tas for ade in a way that it satisfies the initial or bcs exactly an unsupervised error is constructed in approximating the solution of ade which is minimized by training ann using gradient descent algorithm gda two challenging test problems of ade are considered in this paper in which the first problem has steep boundary layers near x 1 and many numerical methods create non physical oscillation near steep boundaries also for the second problem many numerical schemes suffer from computational noise and instability issues the proposed method is advantageous as it does not require temporal discretization for the solution of the ades as well as it does not suffer from numerical instability the reliability and effectiveness of the presented algorithm is investigated by sufficient large number of independent runs and comparison of results with other existing numerical methods the results show that the present method removes the difficulties arising in the solution of the ades and provides solution with good accuracy

radicals of fuzzy ideals abstract there are several natural ways to fuzzify the concepts of prime ideal primary ideal the radical of an ideal and the primary representation of an ideal in a commutative ring in this paper we introduce some new approaches and compare them with known ones our main goal is to unify the various possible fuzzy primary representations of a fuzzy ideal to prepare the way for the study of fuzzy nonlinear systems of equations

a fourth order method of the convection diffusion equations with neumann boundary conditions abstract in this paper we have developed a fourth order compact finite difference scheme for solving the convection diffusion equation with neumann boundary conditions firstly we apply the compact finite difference scheme of fourth order to discrete spatial derivatives at the interior points then we present a new compact finite difference scheme for the boundary points which is also fourth order accurate finally we use a pade approximation method for the resulting linear system of ordinary differential equations the presented scheme has fifth order accuracy in the time direction and fourth order accuracy in the space direction it is shown through analysis that the scheme is unconditionally stable numerical results show that the compact finite difference scheme gives an efficient method for solving the convection diffusion equations with neumann boundary conditions

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

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

numerical modeling of nonlinear acoustic waves in a tube connected with helmholtz resonators acoustic wave propagation in a one dimensional waveguide connected with helmholtz resonators is studied numerically finite amplitude waves and viscous boundary layers are considered the model consists of two coupled evolution equations a nonlinear pde describing nonlinear acoustic waves and a linear ode describing the oscillations in the helmholtz resonators the thermal and viscous losses in the tube and in the necks of the resonators are modeled by fractional derivatives a diffusive representation is followed the convolution kernels are replaced by a finite number of memory variables that satisfy local ordinary differential equations a splitting method is then applied to the evolution equations their propagative part is solved using a standard tvd scheme for hyperbolic equations whereas their diffusive part is solved exactly various strategies are examined to compute the coefficients of the diffusive representation finally an optimization method is preferred to the usual quadrature rules the numerical model is validated by comparisons with exact solutions the properties of the full nonlinear solutions are investigated numerically in particular the existence of acoustic solitary waves is confirmed

primary tl submodules and p primary tl submodules abstract in this paper we introduce the concepts of primary tl submodules and p primary tl submodules of m where m is a module i e left module over a given commutative ring with identity and t an arbitrary infinitely distributive t norm on a given complete brouwerian lattice l we also give complete characterization of primary tl submodules and study the primary decomposition of tl submodules

homotopy perturbation transform method for nonlinear equations using he s polynomials in this paper a combined form of the laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations this method is called the homotopy perturbation transform method hptm the nonlinear terms can be easily handled by the use of he s polynomials the proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round off errors the fact that the proposed technique solves nonlinear problems without using adomian s polynomials can be considered as a clear advantage of this algorithm over the decomposition method