Non-Standard finite difference scheme based on the ta-Method For predator-Prey dynamical system

Abstract

In this thesis, a Non-Standard Finite Difference (NSFD) method based on the θ− method is formulated for solving the mathematical model of the Beddington-DeAngelis functional response predator-prey dynamical system. The NSFD scheme incorporates a time step function, which ensures the preservation of key qualitative features of the continuous system while providing flexibility in handling stiffness. A rigorous linear stability and convergence analysis is conducted to evaluate the scheme’s theoretical properties. This analysis exhibits the advantages of the NSFD method in preserving stability, accuracy, and convergence, making it a robust tool for modeling ecological and dynamical systems. Numerical comparisons between the proposed method and existing methods demonstrate that the new NSFD-based approach exhibits superior accuracy and convergence