An explicit high-order compact finite difference scheme for the three-dimensional acoustic wave equation with variable speed of sound

In this paper, the correction for the remainder of the truncation error of the second-order central difference scheme is employed to discretize temporal derivative, while the fourth-order Padé schemes are directly used to compute spatial derivatives, an explicit high-order compact finite difference scheme to solve the three-dimensional acoustic wave equation with variable speed of sound is proposed. This new scheme has the fourth-order accuracy in both temporal and spatial directions. It has high computational efficiency since the Thomas algorithm is employed to solve three tridiagonal linear systems formed by the Padé schemes on the (n)th time step and then an explicit time advancement process is conducted for the $(n+1)$th time step. The stability and convergence condition of the proposed scheme are proved. We extend the proposed method to solve problems with nonlinear source terms and systems. Numerical experiments are conducted to demonstrate theoretical analysis results of the proposed scheme.