A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866910753092534272 |
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| author | Beauregard, Matthew A. Padgett, Joshua L. |
| author_facet | Beauregard, Matthew A. Padgett, Joshua L. |
| contents | Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self- and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1901_06049 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion Beauregard, Matthew A. Padgett, Joshua L. Numerical Analysis Self- and cross-diffusion are important nonlinear spatial derivative terms that are included into biological models of predator-prey interactions. Self-diffusion models overcrowding effects, while cross-diffusion incorporates the response of one species in light of the concentration of another. In this paper, a novel nonlinear operator splitting method is presented that directly incorporates both self- and cross-diffusion into a computational efficient design. The numerical analysis guarantees the accuracy and demonstrates appropriate criteria for stability. Numerical experiments display its efficiency and accuracy. |
| title | A variable nonlinear splitting algorithm for reaction-diffusion systems with self- and cross-diffusion |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/1901.06049 |