### 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 language | English |
---|---|

Pages (from-to) | 627-640 |

Number of pages | 14 |

Journal | Journal of Nonlinear Science and Applications |

Volume | 9 |

Issue number | 2 |

Publication status | Published - 2016 |

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### 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

*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.

Research output: Contribution to journal › Article

*Journal of Nonlinear Science and Applications*, vol. 9, no. 2, pp. 627-640.

}

TY - JOUR

T1 - Numerical solution of n’th order fuzzy initial value problems by six stages

AU - Jameel, Ali

AU - Anakira, N. R.

AU - Alomari, A. K.

AU - Hashim, Ishak

AU - Shakhatreh, M. A.

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Circuit model problem

KW - Fuzzy differential equations

KW - Fuzzy numbers

KW - Six stages Runge-Kutta method of order five

UR - http://www.scopus.com/inward/record.url?scp=84944755105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84944755105&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84944755105

VL - 9

SP - 627

EP - 640

JO - Journal of Nonlinear Science and Applications

JF - Journal of Nonlinear Science and Applications

SN - 2008-1898

IS - 2

ER -