Nonstandard finite difference method for ODEs for initial-value problems

In this paper, a powerful recent non-standard finite different method by nonlocal approximation is improved. Also, compared standard finite difference method to this non-standard finite different method in terms of stability and accuracy. As a numerical example, Hybrid Selection & Genetics equation is considered as the candidate from class of first order ODEs with polynomial right-hand sides. Furthermore, results obtained from the non-standard finite different method and MATLAB ODE solvers (ode15s,ode23s) compared in terms of stability, accuracy, and execution time.

Keywords:

Nonstandard finite difference method, Nonlocal approximation MATLAB ODE solvers,

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