An efficient method to solve fuzzy Volterra integral equations using Fibonacci polynomials

Abstract

According to a huge interest in implementation of the fuzzy Volterra integral equations, especially the second kind, researchers have been investigating to solve such equations using numerical methods since analytical ones might not be accessible usually. In this research paper, we introduce a new approach based on Fibonacci polynomials collocation method to numerically solve them. Several properties of such polynomials were considered to implement in the collocation method due to approximate the solution of the second kind of fuzzy Volterra integral equations. We approved the existence, uniqueness of the solution, convergence and the error analysis of the proposed method in detail. In order to show the authenticity and applicability of the proposed method, we employed several illustrative examples. The numerical results show that the convergence and precision of the recent method were in a good settlement with the exact solution. Also, the calculations of the suggested method are simple and low computational complexity in respect to other methods as an advantage feature of the presented approach.