Abstract
We discuss an ordinary differential equation system proposed in [1] as a mathematical model for shrinking and stretching motions of elastic materials. Also, a numerical scheme due to the structure-preserving numerical method was constructed. Our aim of this paper is to compare the numerical results for periodic solutions by several methods in order to investigate their accuracy. We note that a proof for existence of periodic solutions of the ODE system is given. Finally, we derive a partial differential equation model from the ODE system and show numerical results for the PDE model.
| Original language | English |
|---|---|
| Pages (from-to) | 387-414 |
| Number of pages | 28 |
| Journal | Advances in Mathematical Sciences and Applications |
| Volume | 30 |
| Issue number | 2 |
| Publication status | Published - 2021 |
Bibliographical note
Funding Information:The work of the second author is partially supported by JSPS KAKENHI Grant Number JP19K03572. We also would like to thank the anonymous reviewers for careful reading, and their suggestions and comments.
Publisher Copyright:
© 2021 Gakko Tosho Co. Ltd.. All right reserved.
Funding
The work of the second author is partially supported by JSPS KAKENHI Grant Number JP19K03572. We also would like to thank the anonymous reviewers for careful reading, and their suggestions and comments.
Keywords
- Elastic material
- periodic solution
- structure-preserving numerical method