2022 Volume 7 Issue 1 Supplementary
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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 in [5]. In this work, we develop this method to 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 reliablity of the generalized The Regularization-Homotopy Method


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