Explicit high-order compact difference method for solving nonlinear hyperbolic equations with three types of boundary conditions

Abstract

In this paper, an explicit compact difference method is constructed to solve nonlinear hyperbolic equations with initial and three types of boundary conditions. Firstly, a nonlinear explicit fourth-order compact difference scheme is derived by truncation error residual correction and the fourth-order Padé approximation. The corresponding scheme for the linear hyperbolic equation is proven to be conditionally stable by the Fourier analysis method. Then, to improve the computational efficiency, the nonlinear scheme is linearized to obtain a linear explicit fourth-order compact difference scheme. Finally, numerical experiments are conducted to verify the stability and accuracy of the presented method.