Galerkin-Chebyshev Pseudo Spectral Method and a Split Step New Approach for a Class of Two dimensional Semi-linear Parabolic Equations of Second Order

Applied Mathematics and Nonlinear Sciences

Talay Akyildiz F.¹  Vajravelu K.² 

[1] Department of Mathematics and Statistics, Faculty of Science, Al-Imam University, Riyadh, Saudi Arabia;Department of Mathematics, University of Central Florida, Orlando, Florida 32816, USA;

关键词: split step method;    semi-linear parabolic equation;    galerkin-chebyshev spectral method;    galerkin-chebyshev pseudo spectral method;    poisson-boltzman model;    365m70;    35k58;    65n06;    65n12;   

DOI  :  10.21042/AMNS.2018.1.00019

来源: DOAJ

【 摘 要 】

In this paper, we use a time splitting method with higher-order accuracy for the solutions (in space variables) of a class of two-dimensional semi-linear parabolic equations. Galerkin-Chebyshev pseudo spectral method is used for discretization of the spatial derivatives, and implicit Euler method is used for temporal discretization. In addition, we use this novel method to solve the well-known semi-linear Poisson-Boltzmann (PB) model equation and obtain solutions with higher-order accuracy. Furthermore, we compare the results obtained by our method for the semi-linear parabolic equation with the available analytical results in the literature for some special cases, and found excellent agreement. Furthermore, our new technique is also applicable for three-dimensional problems.

【 授权许可】

Unknown