On the numerical solutions for a parabolic system with blow-up

AIMS Mathematics

Chien-Hong Cho¹  Ying-Jung Lu² 

[1] 1. Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804, Taiwan;2. Department of Data Application, USI Corporation, Neihu, Taipei 114, Taiwan;

关键词: parabolic system;    blow-up;    finite difference method;    blow-up behavior;    numerical blow-up;   

DOI  :  10.3934/math.2021683

来源: DOAJ

【 摘 要 】

We study the finite difference approximation for axisymmetric solutions of a parabolic system with blow-up. A scheme with adaptive temporal increments is commonly used to compute an approximate blow-up time. There are, however, some limitations to reproduce the blow-up behaviors for such schemes. We thus use an algorithm, in which uniform temporal grids are used, for the computation of the blow-up time and blow-up behaviors. In addition to the convergence of the numerical blow-up time, we also study various blow-up behaviors numerically, including the blow-up set, blow-up rate and blow-up in $ L^\sigma $-norm. Moreover, the relation between blow-up of the exact solution and that of the numerical solution is also analyzed and discussed.

【 授权许可】

Unknown