Stability of difference schemes for two-dimensional parabolic equations with non-local boundary conditions

被引：35

作者：

Ivanauskas, F. ^{[1
,2
]}

Meskauskas, T. ^{[1
]}

Sapagovas, M. ^{[2
]}

机构：

[1] Vilnius State Univ, LT-03225 Vilnius, Lithuania

[2] Inst Informat & Math, LT-08663 Vilnius, Lithuania

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2009年 / 215卷 / 07期

关键词：

Non-local boundary conditions; Parabolic equations; Finite difference schemes; Stepwise stability; STURM-LIOUVILLE OPERATOR; HEAT-EQUATION; NUMERICAL-SOLUTION; KIND;

D O I：

10.1016/j.amc.2009.09.012

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The stability of difference schemes for one-dimensional and two-dimensional parabolic equations, subject to non-local (Bitsadze-Samarskii type) boundary conditions is dealt with. To analyze the stability of difference schemes, the structure of the spectrum of the matrix that defines the linear system of difference equations for a respective stationary problem is studied. Depending on the values of parameters in non-local conditions, this matrix can have one zero, one negative or complex eigenvalues. The stepwise stability is proved and the domain of stability of difference schemes is found. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：2716 / 2732

页数：17

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