In this presentation, we address the numerical solution of the second-order acoustic wave equation using high-order explicit time-integration methods on CPU-GPU architectures. After discretizing the spatial domain with spectral element method, we compare several time-integration schemes for the resulting system of ODEs. We first consider the classical second-order leapfrog method, followed by higher-order Runge-Kutta-Nyström (RKN) schemes and the modified equation approach. We then focus on the analysis of the stability properties of the RKN method. Strategies for incorporating the damping term, which involves the first-order time derivative, are discussed with particular attention to preserving the order of convergence of the schemes. The proposed approaches are compared in terms of computational efficiency, and 3D numerical simulation for the acoustic wave equation are presented.

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