An explicit-implicit Generalized Finite Difference scheme for a parabolic-elliptic density-suppressed motility system
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916105951379456 |
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| author | Herrero-Hervás, Federico |
| author_facet | Herrero-Hervás, Federico |
| contents | In this work, a Generalized Finite Difference (GFD) scheme is presented for effectively computing the numerical solution of a parabolic-elliptic system modelling a bacterial strain with density-suppressed motility. The GFD method is a meshless method known for its simplicity for solving non-linear boundary value problems over irregular geometries. The paper first introduces the basic elements of the GFD method, and then an explicit-implicit scheme is derived. The convergence of the method is proven under a bound for the time step, and an algorithm is provided for its computational implementation. Finally, some examples are considered comparing the results obtained with a regular mesh and an irregular cloud of points. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14693 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An explicit-implicit Generalized Finite Difference scheme for a parabolic-elliptic density-suppressed motility system Herrero-Hervás, Federico Numerical Analysis Analysis of PDEs In this work, a Generalized Finite Difference (GFD) scheme is presented for effectively computing the numerical solution of a parabolic-elliptic system modelling a bacterial strain with density-suppressed motility. The GFD method is a meshless method known for its simplicity for solving non-linear boundary value problems over irregular geometries. The paper first introduces the basic elements of the GFD method, and then an explicit-implicit scheme is derived. The convergence of the method is proven under a bound for the time step, and an algorithm is provided for its computational implementation. Finally, some examples are considered comparing the results obtained with a regular mesh and an irregular cloud of points. |
| title | An explicit-implicit Generalized Finite Difference scheme for a parabolic-elliptic density-suppressed motility system |
| topic | Numerical Analysis Analysis of PDEs |
| url | https://arxiv.org/abs/2401.14693 |