Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations
Provides a rigorous error analysis for a class of numerical integrators for semilinear wave equations, relaxing standard regularity assumptions.
The paper proves optimal second-order convergence for one-stage explicit extended RKN integrators applied to semilinear wave equations, without requiring Lipschitz continuity or higher regularity of the exact solution.
In this paper, we present an error analysis of one-stage explicit extended Runge--Kutta--Nyström integrators for semilinear wave equations. These equations are analysed by using spatial semidiscretizations with periodic boundary conditions in one space dimension. Optimal second-order convergence is proved without requiring Lipschitz continuous and higher regularity of the exact solution. Moreover, the error analysis is not restricted to the spectral semidiscretization in space.