Nonstandard finite difference method for ODEs for initial-value problems

• Main Author: Tarik Celik
• Format: Article
• Language: English
• Published: BİSKA Bilisim Company 2016-10-01
• Series: New Trends in Mathematical Sciences
• Subjects: Nonstandard finite difference method; nonlocal approximation; MATLAB ODE solvers; initial-value problems
• Online Access: https://ntmsci.com/ajaxtool/GetArticleByPublishedArticleId?PublishedArticleId=7196

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.