Crank-Nicolson finite difference method for two-dimensional diffusion with an integral condition

被引：13

作者：

Dehghan, M ^{[1
]}

机构：

[1] Amirkabir Univ technol, Tehran Polytech, Fac Math & Comp Sci, Dept Appl Math, Tehran 15914, Iran

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2001年 / 124卷 / 01期

关键词：

finite difference schemes; numerical integration procedures; diffusion equation; central processor time; non-classic boundary value problems;

D O I：

10.1016/S0096-3003(00)00031-X

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A finite difference method which is based on the (5,5) Crank-Nicolson (CN) scheme is developed for solving the heat equation in two-dimensional space with an integral condition replacing one boundary condition. The fully implicit method developed here, is unconditionally stable and it has reasonable accuracy. While the conditionally stable fully explicit schemes use less amount of central processor (CPU) time; the unconditional stability of the scheme developed in this article for every diffusion number is significant. Some numerical tests are presented and the accuracy obtained and the CPU time required are reported. Error estimates derived in the maximum norm are tabulated. (C) 2001 Elsevier Science Inc. All rights reserved.

引用

页码：17 / 27

页数：11

共 13 条

[1]

Cannon J. R., 1993, Applicable Analysis, V50, P1, DOI 10.1080/00036819308840181

[2] DIFFUSION SUBJECT TO THE SPECIFICATION OF MASS [J].