High Order Compact Explicit Difference Schemes and Stability Analysis for Two-dimensional Wave Equations - SUN Yang; SONG Linlin; AI Xiaohui (Journal of Harbin University of Science and Technology, 2024)
In this paper, a high-order compact explicit finite difference scheme is proposed to numerically solve two-dimensional wave equations with initial boundary value problems. First of all, according to the discrete approximation of derivatives in the existing literature, a sixth-order compact difference scheme with periodic boundary conditions is obtained. Then, in the spatial direction, the derivative term of the boundary node is calculated by substituting the original equation, and the derivative term of the internal node is approximated by the sixth order compact difference formula, so that the spatial accuracy can reach the sixth order. For the time direction, the second-order accuracy difference scheme of the time layer is derived by using the Taylor series expansion formula, the original equation substitution and the central difference formula. In order to improve the overall time accuracy from the second order to the fourth order, the Richardson extrapolation method is used to realize the high-order approximation of the time layer. Furthermore the 1 7 stability of the scheme is analyzed by Fourier analysis method and the stability condition is | a | λ ∈ [0 , ]. Finally, the efficiency and accuracy of the proposed HOCE(6 ,4) scheme are verified by numerical experiments.