The formulation and analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein-Gordon equations

In this paper we focus on the analysis of energy-preserving schemes for solving high-dimensional nonlinear Klein-Gordon equations. A novel energy-preserving scheme is developed based on the discrete gradient method and the Duhamel principle. The local error, global convergence and nonlinear stability of the new scheme are analysed in detail. Numerical experiments are implemented to compare with existing numerical methods in the literature, and the numerical results show the remarkable efficiency of the new energy-preserving scheme presented in this paper.