Numerical technique to solve dynamical system involving fuzzy parameters

Purnima Pandit, Payal Singh

Abstract This paper investigates system of differential equations with fuzzy parameters and fuzzy initial condition i.e. given by ???? ? ????(????) = ???? ???? ????????,???? ???? ????, ???? ???? (????????) =???? ???? ???? for numerical solution. Here ???? ???? ????????,???? ???? ???? can be nonlinear or it can be linear of the form ???? ???? ????? ???? +???? ???? , where ???? ???? ????×???? and ???? ???? ????×???? be some matrices with all entries as fuzzy number. In this paper, we propose the numerical technique which is based on approximation of Hukuhara difference, for both kind of dynamical systems (linear and nonlinear). In dynamical system, uncertainty of possibilistic type can be realized efficiently using fuzzy parameters and such systems are mathematical models for various application in varied domains. For such systems, we get the scheme for existence of solution and its convergence. Lastly, illustrative examples are solved by using proposed scheme and compared with crisp solution. Keywords: Fuzzy parameters, Fuzzy number,Hukuhara differentiability, Linear and nonlinear fuzzy dynamical system.

Title:	Numerical technique to solve dynamical system involving fuzzy parameters
Author Name:	Purnima Pandit, Payal Singh
Abstract:	Abstract This paper investigates system of differential equations with fuzzy parameters and fuzzy initial condition i.e. given by ???? ? ????(????) = ???? ???? ????????,???? ???? ????, ???? ???? (????????) =???? ???? ???? for numerical solution. Here ???? ???? ????????,???? ???? ???? can be nonlinear or it can be linear of the form ???? ???? ????? ???? +???? ???? , where ???? ???? ????×???? and ???? ???? ????×???? be some matrices with all entries as fuzzy number. In this paper, we propose the numerical technique which is based on approximation of Hukuhara difference, for both kind of dynamical systems (linear and nonlinear). In dynamical system, uncertainty of possibilistic type can be realized efficiently using fuzzy parameters and such systems are mathematical models for various application in varied domains. For such systems, we get the scheme for existence of solution and its convergence. Lastly, illustrative examples are solved by using proposed scheme and compared with crisp solution. Keywords: Fuzzy parameters, Fuzzy number,Hukuhara differentiability, Linear and nonlinear fuzzy dynamical system.
Cite this article:	Purnima Pandit, Payal Singh , " Numerical technique to solve dynamical system involving fuzzy parameters " , International Journal of Emerging Trends & Technology in Computer Science (IJETTCS), Volume 6, Issue 4, July - August 2017 , pp. 051-057 , ISSN 2278-6856.
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