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
