Abstract
A Deuflhard-type exponential integrator sine pseudospectral (DEI-SP) method is proposed and analyzed for solving the generalized improved Boussinesq (GIBq) equation. The numerical scheme is based on a second-order exponential integrator for time integration and a sine pseudospectral discretization in space. Rigorous analysis and abundant experiments show that the method converges quadratically and spectrally in time and space, respectively. Finally the DEI-SP method is applied to investigate the complicated and interesting long-time dynamics of the GIBq equation.
| Original language | English |
|---|---|
| Pages (from-to) | 1397-1419 |
| Number of pages | 23 |
| Journal | BIT Numerical Mathematics |
| Volume | 61 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Dec 2021 |
Bibliographical note
Publisher Copyright:© 2021, The Author(s), under exclusive licence to Springer Nature B.V.
Funding
C. Su is supported by the Alexander von Humboldt Foundation. C. Su would like to thank the Isaac Newton Institute for Mathematical Sciences for support and hospitality during the programme Geometry, compatibility and structure preservation in computational differential equations when work on this paper was taken. The second author would like to thank Dr. Ali Shokri for helpful communication.
| Funders | Funder number |
|---|---|
| Alexander von Humboldt-Stiftung |
Keywords
- Error estimate
- Exponential integrator
- Improved Boussinesq equation
- Long-time dynamics
- Sine pseudospectral method