On the dispersion, stability and accuracy of a compact higher-order finite difference scheme for 3D acoustic wave equation

In this paper, we propose a compact fourth-order finite difference scheme with low numerical dispersion to solve the 3D acoustic wave equation. Padé approximation has been used to obtain fourth-order accuracy in both temporal and spatial dimensions, while the alternating direction implicit (ADI) technique has been used to reduce the computational cost. Error analysis has been conducted to show the fourth-order accuracy, which has been confirmed by a numerical example. We have also shown that the proposed method is conditionally stable with a Courant–Friedrichs–Lewy (CFL) condition that is comparable to other existing finite difference schemes. Due to the higher-order accuracy, the new method is found effective in suppressing numerical dispersion.