Compact difference scheme for two-dimensional fourth-order hyperbolic equation

Abstract

In this paper, we mainly study an initial and boundary value problem of a two-dimensional fourth-order hyperbolic equation. Firstly, the fourth-order equation is written as a system of two second-order equations by introducing two new variables. Next, in order to design an implicit compact finite difference scheme for the problem, we apply the compact finite difference operators to obtain a fourth-order discretization for the second-order spatial derivatives and the Crank–Nicolson difference scheme to obtain a second-order discretization for the first-order time derivative. We prove the unconditional stability of the scheme by the Fourier method. Then a convergence analysis is given by the energy method. Numerical results are provided to verify the accuracy and efficiency of this scheme.