full
search.png

Search

close.png

Cancel

arrow
Volume 18, Issue 3
Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings

Zhe Jiao, Yaxu Li & Lijing Zhao

DOI: 10.4208/nmtma.OA-2024-0131

Numer. Math. Theor. Meth. Appl., 18 (2025), pp. 650-679.

Published online: 2025-09

Preview Purchase PDF 128 1495

Cited by

google scholar semantic scholar
Export citation
  • 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 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.

  • Keywords

Semilinear wave equations, nonautonomous damping, dynamic boundary condition, IMEX, error analysis.

  • AMS Subject Headings

65M12, 65M15, 65J08

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{NMTMA-18-650, author = {Jiao , ZheLi , Yaxu and Zhao , Lijing}, title = {Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2025}, volume = {18}, number = {3}, pages = {650--679}, 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 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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2024-0131}, url = {http://global-sci.org/intro/article_detail/nmtma/24322.html} }
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 -

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.

Jiao , ZheLi , Yaxu and Zhao , Lijing. (2025). Implicit-Explicit Time Discretization Schemes for a Class of Semilinear Wave Equations with Nonautonomous Dampings. Numerical Mathematics: Theory, Methods and Applications. 18 (3). 650-679. doi:10.4208/nmtma.OA-2024-0131
Copy to clipboard
BibteX RIS TXT
The citation has been copied to your clipboard