A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866908492498993152 |
|---|---|
| author | Shi, Wei Wang, Bin Liu, Kai |
| author_facet | Shi, Wei Wang, Bin Liu, Kai |
| contents | Many conservative partial differential equations such as the Korteweg-de Vries (KdV) equation, and the nonlinear Schrödinger equations, the Klein-Gordon equation have more than one invariant functionals. In this paper, we propose the definition of the discrete variational derivative, based on which, a novel semi-analytical multiple invariants-preserving integrator for the conservative partial differential equations is constructed by projection technique. The proposed integrators are shown to have the same order of accuracy as the underlying integrators. For applications, some concrete mass-momentum-energy-preserving integrators are derived for the KdV equation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01307 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs Shi, Wei Wang, Bin Liu, Kai Numerical Analysis 65L05, 65L07, 65L20, 65P10, 34C15 Many conservative partial differential equations such as the Korteweg-de Vries (KdV) equation, and the nonlinear Schrödinger equations, the Klein-Gordon equation have more than one invariant functionals. In this paper, we propose the definition of the discrete variational derivative, based on which, a novel semi-analytical multiple invariants-preserving integrator for the conservative partial differential equations is constructed by projection technique. The proposed integrators are shown to have the same order of accuracy as the underlying integrators. For applications, some concrete mass-momentum-energy-preserving integrators are derived for the KdV equation. |
| title | A novel semi-analytical multiple invariants-preserving integrator for conservative PDEs |
| topic | Numerical Analysis 65L05, 65L07, 65L20, 65P10, 34C15 |
| url | https://arxiv.org/abs/2504.01307 |