One-stage explicit trigonometric integrators for effectively solving quasilinear wave equations

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 fully discrete 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.

Automated summary

In this paper, one-stage explicit trigonometric integrators for solving quasilinear wave equations are formulated and studied. The trigonometric integrators are used as the semidiscretization in time, while a spectral Galerkin method is employed for the discretization in space. It is shown that these integrators have second-order convergence in time and the result holds for the fully discrete scheme without requiring any CFL-type coupling.