A Multi-Domain Bivariate Pseudospectral Method for Evolution Equations

被引：6

作者：

Magagula, V. M. ^{[1
]}

Motsa, S. S. ^{[1
]}

Sibanda, P. ^{[1
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Stat & Comp Sci, Private Bag X01, ZA-3209 Pietermaritzburg, South Africa

来源：

INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS | 2017年 / 14卷 / 04期

关键词：

Multi-domain; bivariate interpolation; spectral quasilinearization method; evolution equations; Legendre-Gauss-Lobatto grid points; FITZHUGH-NAGUMO EQUATION; VARIATIONAL ITERATION METHOD; SPECTRAL COLLOCATION METHOD; GENERALIZED BURGER-FISHER; WAVE SOLUTIONS;

D O I：

10.1142/S0219876217500414

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we present a new general approach for solving nonlinear evolution partial differential equations. The novelty of the approach is in the combination of spectral collocation and Lagrange interpolation polynomials with Legendre-Gauss-Lobatto grid points to descritize and solve equations in piece-wise defined intervals. The method is used to solve several nonlinear evolution partial differential equations, namely, the modified KdV-Burgers equation, modified KdV equation, Fisher's equation, Burgers-Fisher equation, Burgers-Huxley equation and the Fitzhugh-Nagumo equation. The results are compared with known analytic solutions to confirm accuracy, convergence and to get a general understanding of the performance of the method. In all the numerical experiments, we report a high degree of accuracy of the numerical solutions. Strategies for implementing various boundary conditions are discussed.

引用

页数：27

共 60 条

[1] Soliton solutions for the Fitzhugh-Nagumo equation with the homotopy analysis method [J].