Numerical blow-up for a nonlinear heat equation

被引：9

作者：

N'Gohisse, Firmin K. ^{[1
]}

Boni, Theodore K. ^{[2
]}

机构：

[1] Univ Abobo Adjame, UFR SFA, Dept Math & Informat, Abidjan 01, Cote Ivoire

[2] Inst Natl Polytech Houphouet Boigny Yamoussoukro, Yamoussoukro, Cote Ivoire

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2011年 / 27卷 / 05期

关键词：

Semidiscretization; blow-up; numerical blow-up time; nonlinear heat equations; SEMILINEAR PARABOLIC EQUATIONS; REACTION-DIFFUSION EQUATIONS; ASYMPTOTIC-BEHAVIOR; TIME; DISCRETIZATIONS; APPROXIMATIONS; 2ND-ORDER; SYSTEM; SETS;

D O I：

10.1007/s10114-011-8464-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper concerns the study of the numerical approximation for the following initialboundary value problem a, u (0) a C (1)([0, 1]), u (0)(0) = 0, u'(0)(1) = 0. We find some conditions under which the solution of a semidiscrete form of the above problem blows up in a finite time and estimate its semidiscrete blow-up time. We also prove the convergence of the semidiscrete blow-up time to the theoretical one. A similar study has been also undertaken for a discrete form of the above problem. Finally, we give some numerical results to illustrate our analysis.

引用

页码：845 / 862

页数：18