DEVELOPMENT OF NEW HARMONIC EULER USING NONSTANDARD FINITE DIFFERENCE TECHNIQUE FOR SOLVING STIFF PROBLEMS

Abstract

Solving stiff problem always required very tiny size of meshes if it is solved via traditional numerical algorithm. Using insufficient of mesh size, will triggered instabilities. In this paper, we develop an algorithm applying Harmonic Mean on Euler method to solve the stiff problems. The main purpose of this paper is to discuss the improvement of Harmonic Euler using Nonstandard Finite Difference (NSFD). The combination of these methods can provide new advantages that Euler method could offer. Four set of stiff problems are solved via three schemes, i.e. Harmonic Euler, Nonstandard Harmonic Euler and Nonstandard EO with Harmonic Euler. Findings show that both nonstandard schemes produce high accuracy results.