One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations
Numerical Analysis
2019-08-27 v4 Numerical Analysis
Abstract
In this paper, one-stage explicit trigonometric integrators for solving quasilinear wave equations are formulated and studied. For solving wave equations, we first introduce trigonometric integrators as the semidiscretization in time and then consider a spectral Galerkin method for the discretization in space. We show that one-stage explicit trigonometric integrators in time have second-order convergence and the result is also true for the fullydiscrete scheme without requiring any CFL-type coupling of the discretization parameters. The results are proved by using energy techniques, which are widely applied in the numerical analysis of methods for partial differential equations.
Cite
@article{arxiv.1811.02252,
title = {One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations},
author = {Bin Wang and Changying Liu and Yonglei Fang},
journal= {arXiv preprint arXiv:1811.02252},
year = {2019}
}