Homotopy analysis method for solving Cauchy integral equations of the first kind

In this paper, by combined homotopy analysis method (HAM) and regularization method we present a new efficient and applicable method and named homotopy regularization method (HRM). For solving Cauchy integral equations of the first kind by using regularization method, we transform the rst kind integral equations to integral equations of the second kind. Then, we apply the homotopy analysis method to solve obtained integral equation. Also, the convergence of the proposed method is proved. An example is solved to show that this method is accurate and effective. Also, by plotting the h-curve, we show the convergence region of the example.