Numerical solution of n’th order fuzzy initial value problems by six stages

Ali Jameel, N. R. Anakira, A. K. Alomari, Ishak Hashim, M. A. Shakhatreh

Research output: Contribution to journalArticle

1 Citation (Scopus)

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 definitions 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.

Original languageEnglish
Pages (from-to)627-640
Number of pages14
JournalJournal of Nonlinear Science and Applications
Volume9
Issue number2
Publication statusPublished - 2016

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Initial Value Problem
Numerical Solution
Fuzzy Set Theory
Runge-Kutta Methods
Ordinary differential equation
First-order
Formulation
Model

Keywords

  • Circuit model problem
  • Fuzzy differential equations
  • Fuzzy numbers
  • Six stages Runge-Kutta method of order five

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Analysis

Cite this

Jameel, A., Anakira, N. R., Alomari, A. K., Hashim, I., & Shakhatreh, M. A. (2016). Numerical solution of n’th order fuzzy initial value problems by six stages. Journal of Nonlinear Science and Applications, 9(2), 627-640.

Numerical solution of n’th order fuzzy initial value problems by six stages. / Jameel, Ali; Anakira, N. R.; Alomari, A. K.; Hashim, Ishak; Shakhatreh, M. A.

In: Journal of Nonlinear Science and Applications, Vol. 9, No. 2, 2016, p. 627-640.

Research output: Contribution to journalArticle

Jameel, A, Anakira, NR, Alomari, AK, Hashim, I & Shakhatreh, MA 2016, 'Numerical solution of n’th order fuzzy initial value problems by six stages', Journal of Nonlinear Science and Applications, vol. 9, no. 2, pp. 627-640.
Jameel, Ali ; Anakira, N. R. ; Alomari, A. K. ; Hashim, Ishak ; Shakhatreh, M. A. / Numerical solution of n’th order fuzzy initial value problems by six stages. In: Journal of Nonlinear Science and Applications. 2016 ; Vol. 9, No. 2. pp. 627-640.
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