Using Wavelet for Numerical Solution of Fredholm Integral Equations

Abstract — In this paper, we bring three theorems that enable us to approximate the solution of Ferdholm integral equations of the second kind. Then we use the Coifman wavelets or Coiflets as scaling functions for projection that satisfied the conditions of theorems for approximation. Also we use this projection to convert the integral equation to a Galerkin system, which is the most important of the expansion methods for solving linear integral equations. Finally, by using numerical examples we show that our estimation have a good degree of accuracy Keywords: Integral Equation, Wavelet, Galerkin System.