Monotone iterative ADI method for semilinear parabolic problems

被引：0

作者：

Boglaev, Igor ^{[1
]}

机构：

[1] Massey Univ, Inst Fundamental Sci, Palmerston North, New Zealand

来源：

BIT NUMERICAL MATHEMATICS | 2015年 / 55卷 / 03期

关键词：

Semilinear parabolic problem; Nonlinear ADI scheme; Upper and lower solutions; Monotone iterations; Monotone iterative ADI method; REACTION-DIFFUSION EQUATIONS; SYSTEMS;

D O I：

10.1007/s10543-014-0529-6

中图分类号：

TP31 [计算机软件];

学科分类号：

081202 ; 0835 ;

摘要：

The paper deals with numerical solving semilinear parabolic problems based on a nonlinear alternating direction implicit (ADI) scheme. The convergence of the nonlinear ADI scheme to the continuous solution is proved. The existence and uniqueness of a solution of the nonlinear ADI scheme are established. A monotone iterative ADI method is constructed. An analysis of convergence of the monotone iterative ADI method to the solution of the nonlinear ADI scheme on the whole time interval is given. Numerical experiments are presented.

引用

页码：647 / 676

页数：30

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