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arXiv · 2410.20784

Implicit-explicit time discretization schemes for a class of semilinear wave equations with nonautonomous dampings

Zhe Jiao·Yaxu Li·Lijing Zhao
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Abstract

This paper is concerned about the implicit-explicit (IMEX) methods for a class of dissipative wave systems with time-varying velocity feedbacks and nonlinear potential energies, equipped with different boundary conditions. Firstly, we approximate the problems by using a vanilla IMEX method, which is a second-order scheme for the problems when the damping terms are time-independent. However, rigors analysis shows that the error rate declines from second to first order due to the nonautonomous dampings. To recover the convergence order, we propose a revised IMEX scheme and apply it to the nonautonomous wave equations with a kinetic boundary condition. Our numerical experiments demonstrate that the revised scheme can not only achieve second-order accuracy but also improve the computational efficiency.

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Zhe Jiao, Yaxu Li, Lijing Zhao. 2024-10-28. Implicit-explicit time discretization schemes for a class of semilinear wave equations with nonautonomous dampings. https://arxiv.org/abs/2410.20784

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