arXiv subjects

Aida Jrajria

Publications and source records attributed to Aida Jrajria.

2 recordsLinked to original sources

arXiv2023

Rescaling method for blow-up solutions of nonlinear wave equations

We develop a hybrid scheme based on a finite difference scheme and a rescaling technique to approximate the solution of nonlinear wave equation. In order to numerically reproduce the blow-up phenomena, we propose a rule of scaling transformation, which is a variant of what was successfully used in the case of nonlinear parabolic equations. A careful study of the convergence of the proposed scheme is carried out and several numerical examples are performed in illustration.

math.NA↗

arXiv2021

Discontinuous Galerkin method for blow-up solutions of nonlinear 1D wave equations

We develop and study a time-space discrete discontinuous Galerkin finite elements method to approximate the solution of one-dimensional nonlinear wave equations. We show that the numerical scheme is stable if a nonuniform time mesh is considered. We also investigate the blow-up phenomena and we prove that under weak convergence assumptions, the numerical blow-up time tends toward the theoretical one. The validity of our results is confirmed throughout several numerical examples and benchmarks.

math.AP↗