Analysis of nonquadratic energy-conservative schemes for KdV type-equations
Fuente:
arXiv
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912162969026560 |
|---|---|
| author | Kawai, Shuto Sato, Shun Matsuo, Takayasu |
| author_facet | Kawai, Shuto Sato, Shun Matsuo, Takayasu |
| contents | Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes remain poorly understood, except in norm-preserving cases.
This study introduces a novel analytical framework applicable to general energy-preserving schemes. The proposed framework is applied to Korteweg-de Vries (KdV)-type equations, establishing global existence and convergence estimates for the numerical solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_15556 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Analysis of nonquadratic energy-conservative schemes for KdV type-equations Kawai, Shuto Sato, Shun Matsuo, Takayasu Numerical Analysis 65M12 Numerical schemes that conserve invariants have demonstrated superior performance in various contexts, and several unified methods have been developed for constructing such schemes. However, the mathematical properties of these schemes remain poorly understood, except in norm-preserving cases. This study introduces a novel analytical framework applicable to general energy-preserving schemes. The proposed framework is applied to Korteweg-de Vries (KdV)-type equations, establishing global existence and convergence estimates for the numerical solutions. |
| title | Analysis of nonquadratic energy-conservative schemes for KdV type-equations |
| topic | Numerical Analysis 65M12 |
| url | https://arxiv.org/abs/2412.15556 |