Two conservative and linearly-implicit compact difference schemes for the nonlinear fourth-order wave equation

Abstract

Two conservative and linearly-implicit difference schemes are presented for solving the nonlinear fourth-order wave equation with the periodic boundary condition. These schemes are based on two different compact finite difference discretization, and they are shown to be fourth-order accurate in space and second-order accurate in time. The discrete energy conservation is obtained for the developed schemes, which preserve the original energy conservation. Meanwhile, two implicit conservative compact difference schemes are also presented. Numerical experiments are given to confirm the theoretical results.