A decoupled and conservative difference scheme with fourth-order accuracy for the Symmetric Regularized Long Wave equations

Abstract

In this paper, a decoupled finite difference scheme with fourth-order accuracy is proposed to solve the Symmetric Regularized Long Wave equation. The scheme is proved to conserve the total energy in the discrete level. Without any restrictions on the grid ratios, the convergence of the difference scheme is proved by utilizing the energy method to be of forth-order in space and second-order in time. A numerical example is given to support the theoretical analysis.