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ISSN No-2031-5063

Vol.1,Issue.III/Sept11pp.1-4

Research Paper

A new approach to solve Fuzzy differential equation by using third order Runge-Kutta method.N. M. DeshmukhDepartment of Engineering Mathematics, Sanjivani rural education society's College of Engineering, Kopargaon

Abstract A solution of first order Fuzzy differential equation is obtained by Runge-Kutta method of third order (iterative method).The new approach presented in this paper gives complete error analysis by very simple and innovative technique Keywords:- Ordinary differential equation, Fuzzy differential equation, Runge- Kutta method.

] Introduction :The concept of Fuzzy differential equation was first introduced by Chang and Zadeh [1].Later Dubois and Prade [2] defined and used the extension principle. Other methods have been discussed by Puri and Ralescu [3].The existence of solutions of Fuzzy differential equation has been studied by several authors [4,5]. Abbasbandy and Allahviranloo [6] developed numerical algorithms for solving Fuzzy differential equation based on Seikala's derivative of the Fuzzy process introduced in [7]. In the present paper ,the Runge-Kutta method of order three to solve Fuzzy differential equation have been established. The structure of the paper is as follows. In the first three sections, Some concepts and introductory materials to deal with the Fuzzy initial value problem have been recalled. In section 4 and 5 Runge-Kutta method of order three and its iterative solution for solving Fuzzy differential equations are presented. The illustration of numerical example is finally given in section 6. 2] Basic concepts and definition:{A triangular Fuzzy number is defined by three real numbers a