Application of Spectral Collocation Method to Dynamic Comprehensive Stability Analysis of Fractional Diffusion-Reaction System

Abstract

In this study, we use the Legendre spectral collocation method to analyze the stability of a system of fractional diffusion-reaction equations, due to its capacity to simulate a variety of biological and physical processes with irregular diffusion properties. It causes that understanding such systems’ long-term behavior requires a study of stability analysis. The stability criteria are rigorously analyzed through mathematical techniques. This is done after discretizing the equations using the Legendre spectral collocation method. With the intention of predicting system dynamics and creating numerical algorithms, our findings offer discernment into the behavior of stability analysis for fractional diffusion-reaction systems.