Abstract
Two numerical schemes, namely, the Taylor expansion and the variational iteration methods, have been implemented to give an approximate solution of the fuzzy linear Volterra integral equation of the second kind. To display the validity and applicability of the numerical methods, one illustrative example with known exact solution is presented. Numerical results show that the convergence and accuracy of these methods were in a good agreement with the exact solution. However, according to comparison of these methods, we conclude that the variational iteration method provides more accurate results.
Highlights
According to comparison of these methods, we conclude that the variational iteration method provides more accurate results
Fuzzy integral equations of the second kind have attracted the attention of many scientists and researchers in recent years
The concept of fuzzy sets was originally introduced by Zadeh [2] and led to the definition of fuzzy numbers and its implementation in fuzzy control [3] and approximate reasoning problems [4]
Summary
Fuzzy integral equations of the second kind have attracted the attention of many scientists and researchers in recent years. These equations appear frequently in fuzzy control, fuzzy finance, approximate reasoning, and economic systems [1]. Numerous methods have been proposed for solving Volterra integral equations [9]. Liao [11] employed the homotopy analysis method to solve nonlinear problems and it has been applied by Abbasbandy [12] to solve fuzzy Volterra integral equations of the second kind. Hamaydi [19] has used various analytical and numerical methods to solve fuzzy Volterra integral equations
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
