| Abstract: |
| The purpose of this talk is to establish numerical methods for computing quenching solutions of one space dimensional nonlinear wave equations with power nonlinearities. We consider a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. To numerically reproduce the quenching phenomena, we propose a rule of scaling transformation, which is a variant of what was successfully used in the case of nonlinear parabolic equations. After having verified the convergence of our proposed schemes, we prove that solutions of those finite-difference schemes actually quench in the corresponding quenching times. Then, we prove that the numerical quenching time converges to the exact quenching time as the discretization parameters tend to zero. Several numerical examples that confirm the validity of our theoretical results are also offered. |
|