Higher-order energy-preserving difference scheme for the fourth-order nonlinear strain wave equation

Abstract

This paper focus on construction of high-order energy-preserving difference scheme for the fourth-order nonlinear strain wave equation with an energy conservation law. This target model is firstly transformed into an equivalent system by using the method of trigonometric scalar auxiliary variables. The resulting equivalent system possess a modified energy conservation law, and a fourth-order difference scheme with analogously discrete energy conservation law is developed based on the resulting equivalent system. The boundedness and convergence of the numerical solutions in the maximum norm are shown. The effectiveness of the difference scheme is verified by several numerical experiments.