A linearized difference scheme for semilinear parabolic equations with nonlinear absorbing boundary conditions

被引：5

作者：

Sun, Zhi-zhong ^{[1
]}

Wu, Xiaonan ^{[2
]}

Zhang, Jiwei ^{[3
]}

Wang, Desheng ^{[3
]}

机构：

[1] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

[2] Hong Kong Baptist Univ, Dept Math, Kwoloon Tong, Hong Kong, Peoples R China

[3] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, Singapore 637371, Singapore

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2012年 / 218卷 / 09期

关键词：

Unified approach; Nonlinear local absorbing boundary conditions; Parabolic problems in unbounded domains; Finite difference scheme; Nonuniform time step; Solvability; Stability; Convergence; BLOW-UP; CRITICAL EXPONENTS; NUMERICAL-METHOD; BEHAVIOR;

D O I：

10.1016/j.amc.2011.10.083

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A novel three level linearized difference scheme is proposed for the semilinear parabolic equation with nonlinear absorbing boundary conditions. The solution of this problem will blow up in finite time. Hence this difference scheme is coupled with an adaptive time step size, i.e., when the solution tends to infinity, the time step size will be smaller and smaller. Furthermore, the solvability, stability and convergence of the difference scheme are proved by the energy method. Numerical experiments are also given to demonstrate the theoretical second order convergence both in time and in space in L-infinity-norm. (C) 2011 Elsevier Inc. All rights reserved.

引用

页码：5187 / 5201

页数：15

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