A Finite Difference Scheme for Blow-Up Solutions of Nonlinear Wave Equations

作     者：Chien-Hong Cho 

作者机构：Research Institute for Mathematical SciencesKyoto UniversityKyoto 606-8502Japan Department of MathematicsNational Chung Cheng UniversityMin-HsiungChia-Yi 621Taiwan 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2010年第3卷第4期

页      面：475-498页

核心收录：

学科分类：0820[工学-石油与天然气工程] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070102[理学-计算数学] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术（可授工学、理学学位）] 

基　　金：supported by the grant NSC 98-2115-M-194-010-MY2 

主　　题：Finite difference method nonlinear wave equation blow up 

摘      要：We consider a finite difference scheme for a nonlinear wave equation, whose solutions may lose their smoothness in finite time, i.e., blow up in finite time. In order to numerically reproduce blow-up solutions, we propose a rule for a time-stepping,which is a variant of what was successfully used in the case of nonlinear parabolic equations. A numerical blow-up time is defined and is proved to converge, under a certain hypothesis, to the real blow-up time as the grid size tends to zero.