Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations
Numerical Analysis
2018-09-18 v1
Abstract
In this paper, we present an error analysis of one-stage explicit extended Runge--Kutta--Nystr\"{o}m 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.
Keywords
Cite
@article{arxiv.1801.02070,
title = {Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations},
author = {Bin Wang and Xinyuan Wu},
journal= {arXiv preprint arXiv:1801.02070},
year = {2018}
}