Implementing Runge-Kutta Method of Sixth-Order for Numerical Solution of Fuzzy Differential Equations

Alsafar, Marwa Muthna; Ibraheem, Kais Ismail

doi:10.33899/edusj.2023.139083.1347

	Implementing Runge-Kutta Method of Sixth-Order for Numerical Solution of Fuzzy Differential Equations
Journal of Education and Science
Article 12, Volume 32, Issue 3, September 2023, Pages 147-155 PDF (756.53 K)
Document Type: Research Paper
DOI: 10.33899/edusj.2023.139083.1347
Authors
Marwa Muthna Alsafar^* ; Kais Ismail Ibraheem
Department of Physics, College of Education for Pure Sciences, University of Mosul, Mosul, Iraq
Abstract
The article talks about the increasing importance of the practical use of fuzzy differential equations in modeling complex problems in various fields, such as science and engineering, as these differential equations allow for obtaining accurate results for systems that suffer from uncertainty or incomplete knowledge. Fuzzy differential equations are a suitable alternative to ordinary differential equations if nullity and ambiguity are present in the problem. The article presents a new method for solving fuzzy differential equations using Seikkala derivative techniques, which is based on the numerical approach used in Sixth's Rang-Kutta method. A comprehensive analysis of errors is presented, and the method is applied to solve some linear and nonlinear Cauchy problems using MATLAB program to obtain accurate numerical results close to the exact solution. The article hopes that it will help enhance the reader's understanding of these modern techniques in solving fuzzy differential equations, and improve the ability to apply them in practical solutions.
Keywords
Fuzzy Differential Equations,,; ,،؛Runge-Kutta,,; ,،؛Seikkala derivative,,; ,،؛Fuzzy number,,; ,،؛A Cauchy Problem,,; ,،؛Membership function

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