An explicit fourth-order energy-preserving scheme for Riesz space fractional nonlinear wave equations

摘要

In this paper, a new explicit fourth-order scheme for solving Riesz space fractional nonlinear wave equations is developed. The scheme is designed by using a novel Riesz space fractional difference operator for spatial discretization and a multidimensional extended Runge–Kutta–Nyström method for time integration. The conservation law of the semi-discrete energy, stability and convergence of the semi-discrete system are investigated. Numerical experiments show the efficiency and energy conservation of the present scheme.