High order positivity-preserving numerical methods for a non-local photochemical model
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909711840837632 |
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| author | Pezzella, Mario |
| author_facet | Pezzella, Mario |
| contents | In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods, encompassing non-standard finite difference schemes, direct quadrature techniques and predictor-corrector approaches. The proposed discretizations guarantee the positivity, monotonicity and boundedness of the solution regardless of the temporal, spatial and frequency stepsizes. Comprehensive numerical experiments confirm the theoretical findings and demonstrate the efficacy of the proposed methods in simulating realistic photochemical phenomena. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2501_04573 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | High order positivity-preserving numerical methods for a non-local photochemical model Pezzella, Mario Numerical Analysis 65R20, 65M15, 65G99, 65Z05, 47H07, 45K05 In this paper we design high-order positivity-preserving approximation schemes for an integro-differential model describing photochemical reactions. Specifically, we introduce and analyze three classes of dynamically consistent methods, encompassing non-standard finite difference schemes, direct quadrature techniques and predictor-corrector approaches. The proposed discretizations guarantee the positivity, monotonicity and boundedness of the solution regardless of the temporal, spatial and frequency stepsizes. Comprehensive numerical experiments confirm the theoretical findings and demonstrate the efficacy of the proposed methods in simulating realistic photochemical phenomena. |
| title | High order positivity-preserving numerical methods for a non-local photochemical model |
| topic | Numerical Analysis 65R20, 65M15, 65G99, 65Z05, 47H07, 45K05 |
| url | https://arxiv.org/abs/2501.04573 |