An explicit fourth-order compact difference scheme for solving the 2D wave equation

Abstract

Abstract In this paper, an explicit fourth-order compact (EFOC) difference scheme is proposed for solving the two-dimensional(2D) wave equation. The truncation error of the EFOC scheme is O ( τ 4 + τ 2 h 2 + h 4 ) $O({\tau ^{4}} + {\tau ^{2}}{h^{2}} + {h^{4}})$ , i.e., the scheme has an overall fourth-order accuracy in both time and space. Because the scheme is explicit, it does not need any iterative processes. Afterwards, the stability condition of the scheme is obtained by using the Fourier analysis method, which has a wider stability range than other explicit or alternation direction implicit (ADI) schemes. Finally, some numerical experiments are carried out to verify the accuracy and stability of the present scheme.

Keywords

• Wave equation
• Padé approximation
• Explicit difference
• High-order compact scheme
• Stability