| Issue |
ESAIM: M2AN
Volume 59, Number 3, May-June 2025
|
|
|---|---|---|
| Page(s) | 1763 - 1790 | |
| DOI | https://doi.org/10.1051/m2an/2025041 | |
| Published online | 26 June 2025 | |
High order positivity-preserving numerical methods for a non-local photochemical model
1
National Research Council of Italy – Institute for Applied Mathematics “Mauro Picone”, Via P. Castellino, 111, 80131 Naples, Italy
2
Member of the INdAM Research Group GNCS
* Corresponding author: mario.pezzella@cnr.it
Received:
9
January
2025
Accepted:
21
May
2025
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.
Mathematics Subject Classification: 65R20 / 65M15 / 65G99 / 65Z05 / 47H07 / 45K05
Key words: Dynamical consistency / positivity-preserving / convergence analysis / non-standard finite differences / direct quadrature / predictor–corrector / Volterra Integro-differential equations
© The authors. Published by EDP Sciences, SMAI 2025
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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