Solving Fuzzy Differential Equations by Runge-kutta Method

Volume 2, Issue 2, pp 208--221 http://dx.doi.org/10.22436/jmcs.002.02.01

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Authors

Z. Akbarzadeh Ghanaie - Mathematics Department, Kerman University and Young Research’s Society of Shahid Bahonar University of Kerman, Kerman, Iran M. Mohseni Moghadam - Center of Excellence of Linear Algebra and Optimization, Shahid Bahonar University of Kerman, Kerman, Iran

Abstract

In this paper, we interpret a fuzzy differential equation (FDE) by using the strongly generalized differentiability concept. Then we show that by this concept any FDE can be transformed to a system of ordinary differential equations (ODEs). Next by solving the associate ODEs we will find two solutions for FDE. Here we express the generalized Runge-Kutta approximation method of order two and analyze its error. Finally one example in the nuclear decay equation show the rich behavior of the method.

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Keywords

• fuzzy differential equation
• generalized differentiability
• generalized Runge-Kutta method.

MSC

•  34A07
•  65L06
•  03E72

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