Error analysis of one-stage explicit extended RKN integrators for semilinear wave equations

Abstract

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.

References in corpus (2)

• Exponential integrators preserving first integrals or Lyapunov functions for conservative or dissipative systems
• Trigonometric collocation methods based on Lagrange basis polynomials for multi-frequency oscillatory second-order differential equations

Cited by in corpus (1)

• Exponential integrators for second-order in time partial differential equations