A numerical solution of Burgers’ equation by pseudospectral method and Darvishi’s preconditioning

A differential quadrature based numerical method for highly accurate solutions of Burgers' equation

“…Error in and are computed and presented in Tables and . Table is used for the comparison of errors with that of pseudospectral method . In , Darvishi et al have taken Eq.…”

“…Table is used for the comparison of errors with that of pseudospectral method . In , Darvishi et al have taken Eq. (25) without any division by for the evaluation error, and hence in the present scheme for Table .…”

“…Error in L 2 and L ∞ are computed and presented in Tables V and VI. Table V is used for the comparison of errors with that of pseudospectral method [61]. In [61], Darvishi PDQ [40] PDQ-TS [58] PDQ [40] PDQ-TS [58] PDQ [40] PDQ-TS [42].…”

Contemporary review of techniques for the solution of nonlinear Burgers equation

“…They also solved the problem by time discretization of Adomain's decomposition method in [93]. Darvishi and Javidi [94] studied a numerical solution of Burgers equation by pseudospectral method and Darvishi's preconditioning. Bratsos [95] solved modified Burgers equation by a finite difference scheme based on fourth order rational approximants to the matrix exponential term in a two time level recurrence relation.…”

Numerical solution of Burgers equation with nonlinear damping using non-polynomial tension spline

“…Different numerical technique have been used for solving Burgers equation.Finite difference methods have been given by Biringen et al [4] and Kutluay et al [25]and recently,by Inan et al [21].Finite elements methods have been given by Caldwell et al [9]and Varglu et al [42] and Ozis et al [35].Spectral methods have been developed by Bar-yoseph et al [5]and Mansell et al [32].Pseudo-spectral method has been used by Darvishi et al [12] and distributed approximation function approach has studied by Zang et al [47] and Wei et al [44].Boundary elements methods is given by Bahadir et al [6].A wavelet collocation method has used by Garba [17],furthermore quasi wavelet based numerical method has been suggested by Wan et al [45].Fast adaptive diffusion wavelet method have been survived by Goyal et al [18].Least square quadratic B-spline finite elements has been given by Kutluay et al [26].Various B-spline have been proposed by Dag et al [13,41].B-spline and multi-quadratic quasi-interpolation have been described by Zhu et al and Chen et al [48,10]. The present work attempts to use cubic non-polynomial spline [36,19,33].One of the important ability of this approximation is the tension parameters involving definition of non-polynomial cubic spline which can be chosen in such a way that the local truncation error of the proposed method can be optimal.Hence,it has been demonstrate that tension spline give better result.This paper is organized as follows:In section 2,derivation and formulation of the cubic non-polynomial tension spline along with consistency relation of second derivatives discussed in details.In section 3,the derivation of two level scheme based on non-polynomial tension spline has been described.In section 4,convergence analysis of the present method has been discussed in detail and we have shown under appropriate condition the method converges.At the end,we illustrate the accuracy and efficiency of the proposed method by testing this approach on two test problems.comparison of the numerical result are given.…”