The Use of Homotopy Regularization Method for Linere and Nonlinner Fredholm Integral Equations of the First Kind

Abstract

Recently, Wazwaz has studied the regularization method to the one-dimensional linear Fredholm integral equations of the first kind [Wazwaz, 2011]. In this work, we develop this method for the linear and nonlinear two-dimensional Fred-holm integral equations of the first kind. Indeed, the regularization method is used for linear integral equations directly. But nonlinear integral equations of the first kind are transformed to linearintegral equations of the first kind by a change of variable; then, The Regularization-Homotopy Method is applied. The combination of the regularization method and the homotopy perturbation method, or shortly, the regularization-homotopy method, is used to find a solution to the equation. Some examples will be used to highlight the reliability of the generalized of Regularization-Homotopy Method.