High order positivity-preserving numerical methods for a non-local photochemical model

TL;DR

This paper develops high-order numerical methods that preserve positivity for a complex non-local photochemical model, ensuring accurate and stable simulations of photochemical reactions.

Contribution

The paper introduces three classes of positivity-preserving schemes—finite difference, quadrature, and predictor-corrector—for integro-differential photochemical models.

Findings

Methods guarantee positivity, monotonicity, and boundedness.

Numerical experiments confirm theoretical properties.

Proposed schemes effectively simulate realistic photochemical phenomena.

Abstract

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.