Modified Patankar Linear Multistep methods for production-destruction systems
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929698959785984 |
|---|---|
| author | Izzo, Giuseppe Messina, Eleonora Pezzella, Mario Vecchio, Antonia |
| author_facet | Izzo, Giuseppe Messina, Eleonora Pezzella, Mario Vecchio, Antonia |
| contents | Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weight denominators to achieve it. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_12540 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified Patankar Linear Multistep methods for production-destruction systems Izzo, Giuseppe Messina, Eleonora Pezzella, Mario Vecchio, Antonia Numerical Analysis Dynamical Systems 65L05 (Primary) 65L06, 34B18 (Secondary) Modified Patankar schemes are linearly implicit time integration methods designed to be unconditionally positive and conservative. In the present work we extend the Patankar-type approach to linear multistep methods and prove that the resulting discretizations retain, with no restrictions on the step size, the positivity of the solution and the linear invariant of the continuous-time system. Moreover, we provide results on arbitrarily high order of convergence and we introduce an embedding technique for the Patankar weight denominators to achieve it. |
| title | Modified Patankar Linear Multistep methods for production-destruction systems |
| topic | Numerical Analysis Dynamical Systems 65L05 (Primary) 65L06, 34B18 (Secondary) |
| url | https://arxiv.org/abs/2407.12540 |