Mathematics and Statistics Vol. 9(3), pp. 350 - 356
DOI: 10.13189/ms.2021.090317
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Numerical Treatment for Solving Fuzzy Volterra Integral Equation by Sixth Order Runge-Kutta Method

Rawaa Ibrahim Esa ¹, Rasha H Ibraheem ², Al.i F Jameel ^3,*
1 Department of Computer Science, College of Basic Education, Al-Mustansiriyah University, Baghdad, Iraq
² Department of Mathematics, College of Basic Education, Al-Mustansiriyah University, Baghdad, Iraq
³ School of Quantitative Sciences, College of Arts and Sciences, University Utara Malaysia, Sintok, Kedah, Malaysia

ABSTRACT

There has recently been considerable focus on finding reliable and more effective numerical methods for solving different mathematical problems with integral equations. The Runge–Kutta methods in numerical analysis are a family of iterative methods, both implicit and explicit, with different orders of accuracy, used in temporal and modification for the numerical solutions of integral equations. Fuzzy Integral equations (known as FIEs) make extensive use of many scientific analysis and engineering applications. They appear because of the incomplete information from their mathematical models and their parameters under fuzzy domain. In this paper, the sixth order Runge-Kutta is used to solve second-kind fuzzy Volterra integral equations numerically. The proposed method is reformulated and updated for solving fuzzy second-kind Volterra integral equations in general form by using properties and descriptions of fuzzy set theory. Furthermore a Volterra fuzzy integral equation, based on the parametric form of a fuzzy numbers, transforms into two integral equations of the second kind in the crisp case under fuzzy properties. We apply our modified method using the specific example with a linear fuzzy integral Volterra equation to illustrate the strengths and accurateness of this process. A comparison of evaluated numerical results with the exact solution for each fuzzy level set is displayed in the form of table and figures. Such results indicate that the proposed approach is remarkably feasible and easy to use.

KEYWORDS
Fuzzy Numbers, Fuzzy α-Level Sets, Fuzzy Integrals, Second-Class Fuzzy Volterra Integral Equations (FVIE2), Sixth Order Range -Kutta Method (RKM6)

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Rawaa Ibrahim Esa , Rasha H Ibraheem , Al.i F Jameel , "Numerical Treatment for Solving Fuzzy Volterra Integral Equation by Sixth Order Runge-Kutta Method," Mathematics and Statistics, Vol. 9, No. 3, pp. 350 - 356, 2021. DOI: 10.13189/ms.2021.090317.

(b). APA Format:
Rawaa Ibrahim Esa , Rasha H Ibraheem , Al.i F Jameel (2021). Numerical Treatment for Solving Fuzzy Volterra Integral Equation by Sixth Order Runge-Kutta Method. Mathematics and Statistics, 9(3), 350 - 356. DOI: 10.13189/ms.2021.090317.