Blow-Up of Finite-Difference Solutions to Nonlinear Wave Equations

Journal of Mathematical Sciences

Sasaki, Takiko¹  Saito, Norikazu¹ 

关键词: Nonlinear wave equation;    blow-up;    finite-difference method.;   

DOI  :  

学科分类：数学（综合）

来源: University of Tokyo * Department of Mathematical Sciences

【 摘 要 】

Finite-differenceschemesforcomputingblow-upsolutionsofonedimensionalnonlinearwaveequationsarepresented.Byapplyingtimeincrementscontroltechnique,wecanintroduceanumericalblow-uptimewhichisanapproximationoftheexactblow-uptimeofthenonlinearwaveequation.Afterhavingverifiedtheconvergenceofourproposedschemes,weprovethatsolutionsofthosefinite-differenceschemesactuallyblowupinthecorrespondingnumericalblow-uptimes.Then,weprovethatthenumericalblow-uptimeconvergestotheexactblow-uptimeasthediscretizationparameterstendtozero.Severalnumericalexamplesthatconfirmthevalidityofourtheoreticalresultsarealsooffered.

【 授权许可】

Unknown