An accurate double Chebyshev spectral approximation for parabolic partial differential equations
type: Item
instance of: scholarly article
title: An accurate double Chebyshev spectral approximation for parabolic partial differential equations
zbMATH Open document ID: 0899.65060
published in: Journal of the Egyptian Mathematical Society
publication date: 1998-10-27T00:00:00Z
review text: Spectral methods based on double Chebyshev expansion for solving numerically partial differential equations have been used by many authors. In this paper two alternative methods are developed, which reduce a parabolic partial differential equation in two space variables in a square subjected to the most general inhomogeneous mixed boundary and initial conditions to a system of ordinary differential equations in the spectral Chebyshev expansion coefficients. This system is greatly simplified by using the Kronecker matrix algebra and it is solved by the step-by-step method. Numerical results show that both methods compare favourably with the theoretical solution.
Mathematics Subject Classification ID: 65M70
Mathematics Subject Classification ID: 35K15
zbMATH DE Number: 1092971
zbMATH Keywords: parabolic partial differential equation
zbMATH Keywords: spectral methods
zbMATH Keywords: double Chebyshev series method
zbMATH Keywords: Kronecker matrix algebra
zbMATH Keywords: numerical examples
author: E. H. Doha
author: M. A. Helal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1092971