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.Several numerical examples that confirm the validity of our theoretical results are also offered.
|Number of pages||32|
|Journal||Journal of Mathematical Sciences (Japan)|
|Publication status||Published - 2016 Jan 1|
- Finite-difference method
- Nonlinear wave equation
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