Numerical Solution of Fuzzy Linear Volterra Integral Equations of the Second Kind by Homotopy Analysis Method

The integral equations arise in many industrial fields, such as: electromagnetic fields andthermal problems. It is well-known that the problem of heat conduction with a variableheat transfer coefficient is reduced to the solution of a Volterra integral equation of second kind. In this paper, we focus on fuzzy linear Volterra integral equations of the second kind and propose a new method to solve them, namely “homotopy analysis method” (HAM). It is found that the HAM provides us with a simple way to adjust and control the convergence region of solution series by introducing an auxiliary parameter ~. The results illustrate the utility and the great potential of the HAM to solve fuzzy integral equations.