Abstract
In this paper, we derive a new exponential wave integrator sine pseudo-spectral (EWI-SP) method for the higher-order Boussinesq equation involving the higher-order effects of dispersion. The method is fully-explicit and it has fourth order accuracy in time and spectral accuracy in space. We rigorously carry out error analysis and establish error bounds in the Sobolev spaces. The performance of the EWI-SP method is illustrated by examining the long-time evolution of the single solitary wave, single wave splitting, and head-on collision of solitary waves. Numerical experiments confirm the theoretical results.
| Original language | English |
|---|---|
| Pages (from-to) | 1583-1606 |
| Number of pages | 24 |
| Journal | Numerical Algorithms |
| Volume | 97 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 2024 |
Bibliographical note
Publisher Copyright:© The Author(s) 2024.
Funding
The authors would like to express sincere gratitude to the reviewers and the editor for their constructive suggestions which helped to improve the quality of this paper. Melih Cem Canak was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the grant 2210. This work was also supported by the Research Fund of the Istanbul Technical University. Project Number: 43325. Open access funding provided by the Scientific and Technological Research Council of Türkiye (TÜBİTAK). Melih Cem Canak was supported by the Scientific and Technological Research Council of Turkey (TUBITAK) under the grant 2210. This work was also supported by the Research Fund of the Istanbul Technical University. Project Number: 43325.
| Funders | Funder number |
|---|---|
| Türkiye Bilimsel ve Teknolojik Araştırma Kurumu | 2210 |
| Istanbul Teknik Üniversitesi | 43325 |
Keywords
- Error estimate
- Exponential integrator
- Higher-order Boussinesq equation
- Long-time dynamics
- Sine pseudo-spectral method