A novel method to solve fuzzy Volterra integral equations using collocation method

Subject Areas : Fuzzy Sets and Systems

Nouredin  Parandin ¹ (Department of Mathematics, Islamic Azad University, Kermanshah Branch, kermanshah, Iran)
Mohsen  Darabi ² (Department of Mathematics, Islamic Azad University, Kermanshah Branch, kermanshah, Iran)

Received: 2022-02-04 Accepted : 2022-03-20 Published : 2020-12-01

Keywords: Fuzzy Volterra integral equation, Fibonacci polynomial, collocation method,

Abstract :

Fuzzy Volterra integral equations, especially the second kind is interested for researchers to be solved withnumerical methods since analytical methods are not applicable. Here a new study based on Fibonacci polynomialscollocation method in order to solve them is introduced. Some properties of these polynomials are consideredto implement a collocation method in order to approximate the solution of Fuzzy Volterra integral equations ofthe second kind. The existence and uniqueness of the solution also convergence and error analysis of proposedmethod are proved thoroughly. The results showed the calculations of the method are simple and low cost.