TY - JOUR
T1 - Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings
AU - Jiao , Zhe
AU - Li , Yaxu
AU - Zhao , Lijing
JO - Numerical Mathematics: Theory, Methods and Applications
VL - 3
SP - 650
EP - 679
PY - 2025
DA - 2025/09
SN - 18
DO - http://doi.org/10.4208/nmtma.OA-2024-0131
UR - https://global-sci.org/intro/article_detail/nmtma/24322.html
KW - Semilinear wave equations, nonautonomous damping, dynamic boundary condition, IMEX, error analysis.
AB - <p style="text-align: justify;">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 the Hochbruck-Leibold 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 modified IMEX scheme and apply it to the nonautonomous wave
equations with a kinetic boundary condition. Our numerical experiments demonstrate that the modified scheme can not only achieve second-order accuracy but also
improve the computational efficiency.</p>