Time fourth-order energy-preserving AVF finite difference method for nonlinear space-fractional wave equations

Abstract

In this paper, we develop and analyze a new time fourth-order energy-preserving average vector field (AVF) finite difference method for the nonlinear fractional wave equations with Riesz space-fractional derivative. To the corresponding Hamiltonian system of the nonlinear fractional wave equations, the fourth-order weighted and shifted Lubich difference operator in space and the fourth-order AVF method in time are used to develop the time fourth-order energy-preserving AVF finite difference method for the nonlinear fractional wave equations. The energy conservation in the discrete form and unique solvability of the proposed scheme are proved and error estimates of the scheme are further proved to be order of O((Δt)4+h4) in the discrete L2- norm. Numerical experiments confirm energy conservation and high-order accuracy of the proposed scheme.