Numerical Solution of Fuzzy Second Kind Fredholm Integral Equations in Double Parametric Form of Fuzzy Number

Hamzeh Zureigat^1,*

¹Department of Mathematics, Faculty of Science and Technology, Jadara University, 21110 Irbid, Jordan

Email: hamzeh.zu@ jadara.edu.jo  

Abstract

In this paper, two numerical methods that are method of successive approximations and Fredholm’s first fundamental theorem are developed, reformatted, and applied to solve fuzzy second kind Fredholm integral equations with a separable kernel. The fuzziness in the equations is represented utilizing convex normalized triangular fuzzy numbers, which are based on a single and double parametric form of fuzzy numbers. A comparative analysis study between the proposed schemes are discussed through numerical experiment. It was found that Fredholm's first fundamental theorem is more efficient and effective than method of successive approximations. Furthermore, the double parametric form of fuzzy number is a general and more reliable than single parametric form since it reduced the computational cost and provides more certain fuzzy cases.

Keywords: Fuzzy Fredholm integral equations; Successive approximations; Fredholm’s first fundamental method; Numerical methods