Numerical solution of nth order fuzzy initial value problems by six stages

Volume 9, Issue 2, pp 627--640 http://dx.doi.org/10.22436/jnsa.009.02.26

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Authors

A. Jameel - School of Quantitative Sciences, Universiti Utara Malaysia (UUM), Kedah, Sintok, 06010, Malaysia. N. R. Anakira - Department of Mathematics, Faculty of Science and Technology, Irbid National University, 2600 Irbid, Jordan. A. K. Alomari - Department of Mathematics, Faculty of Science, Yarmouk University, 211-63 Irbid, Jordan. I. Hashim - School of Mathematical Sciences, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia. M. A. Shakhatreh - Department of Mathematics, Faculty of Science, Yarmouk University, 211-63 Irbid, Jordan.

Abstract

The purpose of this paper is to present a numerical approach to solve fuzzy initial value problems (FIVPs) involving n-th order ordinary differential equations. The idea is based on the formulation of the six stages Runge-Kutta method of order five (RKM56) from crisp environment to fuzzy environment followed by the stability deffnitions and the convergence proof. It is shown that the n-th order FIVP can be solved by RKM56 by transforming the original problem into a system of first-order FIVPs. The results indicate that the method is very effective and simple to apply. An efficient procedure is proposed of RKM56 on the basis of the principles and definitions of fuzzy sets theory and the capability of the method is illustrated by solving second-order linear FIVP involving a circuit model problem.

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Keywords

• Fuzzy numbers
• fuzzy differential equations
• circuit model problem
• six stages Runge-Kutta method of order five.

MSC

•  34A07
•  65K15
•  03B52

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