An efficient high-order explicit scheme for solving Hamiltonian nonlinear wave equations

Abstract

In this work, we propose and analyze a novel high-order explicit scheme for efficiently solving Hamiltonian nonlinear wave equations. The new explicit scheme is based on the blend of a fourth-order finite difference scheme for spatial discretization and a multidimensional extended Runge–Kutta–Nyström (ERKN) method for time integration, respectively. The conservation law of the semi-discrete energy is established. The stability and convergence of the semidiscretization are examined. The results of numerical experiments show that the blend of the finite difference approximation and multidimensional ERKN method gives an efficient high-order explicit scheme for Hamiltonian nonlinear wave equations in comparison with some existing methods.