Numerical solution of the heat equation with nonlocal boundary conditions

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:110

Article

Liu, YK

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

DOI  :  10.1016/S0377-0427(99)00200-9

来源: Elsevier

【 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.

【 授权许可】

Free