Decoupled algorithms for non-linearly coupled reaction-diffusion competition model with harvesting and Stocking

TL;DR

This paper introduces two new fully discrete decoupled algorithms for a complex reaction-diffusion competition model with harvesting or stocking, demonstrating their stability, accuracy, and effectiveness through rigorous analysis and numerical tests.

Contribution

The paper presents novel first and second order accurate decoupled linearized algorithms for a nonlinearly coupled reaction-diffusion model with harvesting and stocking, with proven stability and convergence.

Findings

Algorithms are stable and optimally accurate in space and time.

Numerical experiments confirm theoretical convergence rates.

Harvesting and stocking influence species coexistence dynamics.

Abstract

We propose, analyze and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled reaction-diffusion $N$-species competition model with harvesting or stocking effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proven rigorously. We verify the predicted convergence rates of our analysis and efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically, and observe the co-existence scenario subject to optimal harvesting or stocking.