Numerical simulation of wave propagation by using a hybrid method with an arbitrary order accuracy in both spatial and temporal approximations

•A numerical method is developed for wave propagation phenomena in isotropic media.•An improved strategy is adopted for precisely implementing boundary conditions.•The method can achieve arbitrary order accuracy in both spatial and temporal approximations.•The method performs well in long-time numerical simulations with large time step. This paper introduces an innovative numerical methodology designed to achieve high precision solution of acoustic wave propagation problem in isotropic material. During the temporal discretization process, the Krylov deferred correction (KDC) technique is employed, wherein a new variable is introduced to handle the second-order time derivative in the governing equations. An improved strategy is adopted for precisely implementing boundary conditions. Following this, the arbitrary-order generalized finite difference method (GFDM) is employed to simulate the transformed boundary value problem at each time step, enabling our framework to select the Taylor series expansion order arbitrarily. Ultimately, a hybrid numerical approach for wave problems is developed to achieve arbitrary-order accuracy in both spatial and temporal approximations. The developed scheme undergoes validation through four different numerical experiments in two- or three-dimension, wherein the numerical solutions obtained are compared with either analytical solutions or results from COMSOL software.