Third-order composite Runge Kutta method for solving fuzzy differential equations

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1 Citation (Scopus)

Abstract

In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examples are given to illustrate the accuracy of the method. The comparisons with the existing method are also discussed. Based on the results, the proposed method gives the better result. Hence, the method can be used to solve fuzzy differential equations.

Original languageEnglish
Pages (from-to)2753-2764
Number of pages12
JournalGlobal Journal of Pure and Applied Mathematics
Volume12
Issue number3
Publication statusPublished - 2016

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Fuzzy Differential Equations
Runge Kutta methods
Runge-Kutta Methods
Differential equations
Composite
Composite materials
Explicit Methods
Differentiability
Numerical Examples
Theorem

Keywords

  • Fuzzy differential equations
  • Hukuhara differentiability
  • Runge-Kutta

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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title = "Third-order composite Runge Kutta method for solving fuzzy differential equations",
abstract = "In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examples are given to illustrate the accuracy of the method. The comparisons with the existing method are also discussed. Based on the results, the proposed method gives the better result. Hence, the method can be used to solve fuzzy differential equations.",
keywords = "Fuzzy differential equations, Hukuhara differentiability, Runge-Kutta",
author = "A. Ramli and Ahmad, {Rokiah @ Rozita} and Din, {Ummul Khair Salma} and Salleh, {Abdul Razak}",
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AU - Ramli, A.

AU - Ahmad, Rokiah @ Rozita

AU - Din, Ummul Khair Salma

AU - Salleh, Abdul Razak

PY - 2016

Y1 - 2016

N2 - In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examples are given to illustrate the accuracy of the method. The comparisons with the existing method are also discussed. Based on the results, the proposed method gives the better result. Hence, the method can be used to solve fuzzy differential equations.

AB - In this paper a third-order composite Runge Kutta method is applied for solving fuzzy differential equations based on generalized Hukuhara differentiability. This study intends to explore the explicit methods which can be improved and modified to solve fuzzy differential equations. Some definitions and theorem are reviewed as a basis in solving fuzzy differential equations. Some numerical examples are given to illustrate the accuracy of the method. The comparisons with the existing method are also discussed. Based on the results, the proposed method gives the better result. Hence, the method can be used to solve fuzzy differential equations.

KW - Fuzzy differential equations

KW - Hukuhara differentiability

KW - Runge-Kutta

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