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A high accuracy method for long-time evolution of acoustic wave equation. (English) Zbl 1448.35325
Summary: This paper makes a first attempt to investigate the long-time behaviour of solutions of 2D acoustic wave equation by integrating strengths of the Krylov deferred correction (KDC) method in temporal direction and the meshless generalized finite difference method (GFDM) in space domain. The KDC approach introduces the second order time derivative of acoustic pressure as a new unknown variable, and then converts the acoustic wave equation into the Helmholtz-type equation with the new variable through the temporal discretization. We finally solve the transformed equation in space domain by employing the meshless GFDM. Numerical experiments are provided to verify the accuracy of the proposed method, and numerical results illustrate the good performance of the method for long-time numerical simulations of acoustic wave problems.

MSC:
35L05 Wave equation
35B40 Asymptotic behavior of solutions to PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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