A class of alternating group explicit finite difference method for diffusion equation
type: Item
instance of: scholarly article
title: A class of alternating group explicit finite difference method for diffusion equation
zbMATH Open document ID: 1203.65134
author: Qing-Hua Feng
published in: Vietnam Journal of Mathematics
publication date: 2009-09-22T00:00:00Z
review text: Using six grid points, the author constructs an implicit finite difference scheme with parameters for the diffusion problem \({\partial u\over\partial t}= a{\partial^2 u\over\partial x^2}\), \(u(x,0)= f(x)\), \(u(0,t)= g_1(t)\), \(u(1,t)= g_2(t)\) on the rectangle \([0,1]\times [0,T]\). Choosing adequately the parameters one obtains the truncation error \(O(\tau^2+ h^4)\) of the scheme, where \(\tau\) and \(h\) are temporal and spatial step sizes, respectively. Next four asymmetry difference schemes are presented and based on them a class of alternating group explicit method is proposed. It is proved unconditionally stability (so by Lax theorem also convergence) to the method. Two numerical examples demonstrates high accuracy of the method.
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 74S20
zbMATH DE Number: 5606219
zbMATH Keywords: diffusion equation
zbMATH Keywords: alternating group explicit finite difference method
zbMATH Keywords: stability of difference method
reviewed by: S. Burys
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5606219