Numerical solution of the heat equation with nonlocal boundary conditions

被引：68

作者：

Liu, YK ^{[1
]}

机构：

[1] Univ Loughborough, Dept Math Sci, Loughborough LE11 3TU, Leics, England

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 1999年 / 110卷 / 01期

关键词：

heat equation; nonlocal boundary condition; theta-method; stability; efficient algorithm;

D O I：

10.1016/S0377-0427(99)00200-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The theta-method for the heat equation with nonlocal boundary conditions is discussed in this paper. The unconditional stability is proved for theta greater than or equal to 1/2, subject to a condition that is much weaker than the one assumed in a paper by Ekolin. Due to the nonlocal boundary conditions, the systems of linear equations generated by the theta-method have a coefficient matrix that is tridiagonal except its first and last rows. Three efficient algorithms for solving this kind of linear systems are presented. A simple numerical example is given to compare their efficiency. (C) 1999 Elsevier Science B.V. All rights reserved.

引用

页码：115 / 127

页数：13

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