Blow-Up of Finite-Difference Solutions to Nonlinear Wave Equations
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Finite-difference schemes for computing blow-up solutions of one dimensional nonlinear wave equations are presented. By applying time increments control technique, we can introduce a numerical blow-up time which is an approximation of the exact blowup time of the nonlinear wave equation. After having verified the convergence of our proposed schemes, we prove that solutions of those finite-difference schemes actually blow up in the corresponding numerical blow-up times.Then, we prove that the numerical blow-up time converges to the exact blow-up time as the discretization parameters tend to zero.Sev eral numerical examples that confirm the validity of our theoretical results are also offered.
- Journal of mathematical sciences, the University of Tokyo
Journal of mathematical sciences, the University of Tokyo 23(1), 349-380, 2016-01-25
Graduate School of Mathematical Sciences, The University of Tokyo