Solutıon of Dıfferentıal Equatıons Usıng Nonstandard Fınıte Dıfference Methods

Abstract

Differential equations are mostly used to model real life problems. However, it is known that in general, these equations do not have complete solutions. For that reason, researchers have tried to solve these problems by means of several numerical methods. Among them, standard finite difference (SFD) is a frequently used method in order to obtain numerical solutions of differential equation for a long time. However, there are many mathematical problems for which the SFD models do not perform well. In recent years, nonstandard finite difference (NSFD) method which gets main motivation from SFD method has been applied to various mathematical models for the purpose of getting reliable numerical results.