Abstract
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.
Original language | English |
---|---|
Pages (from-to) | 349-380 |
Number of pages | 32 |
Journal | Journal of Mathematical Sciences (Japan) |
Volume | 23 |
Issue number | 1 |
Publication status | Published - 2016 Jan 1 |
Externally published | Yes |
Keywords
- Blow-up
- Finite-difference method
- Nonlinear wave equation
ASJC Scopus subject areas
- Mathematics(all)