Numerical solution of the heat equation with nonlinear boundary conditions in unbounded domains

被引：3

作者：

Koleva, Migiena ^{[1
]}

Vulkov, Lubin ^{[1
]}

机构：

[1] Univ Rousse, Ctr Appl Math & Informat, Rousse 7017, Bulgaria

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2007年 / 23卷 / 02期

关键词：

heat equation; nonlinear boundary conditions; unbounded domains; artificial boundary conditions; finite element schemes; numerical blow-up;

D O I：

10.1002/num.20183

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The numerical solution of the heat equation in unbounded domains (for a 1D problem-semi-infinite line and for a 2D one semi-infinite strip) is considered. The artificial boundaries are introduced and the exact artificial boundary conditions are derived. The original problems are transformed into problems on finite domains. The space semi-discretization by finite element method and the full approximation by the implicit-explicit Euler's method are presented. The solvability of the full discretization schemes is analyzed. Computational examples demonstrate the accuracy and the efficiency of the algorithms. Also, the behavior of blowing up solutions is examined numerically. (c) 2006 Wiley Periodicals, Inc.

引用

页码：379 / 399

页数：21

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