A novel technique based on the homotopy analysis method to solve the first kind Cauchy integral equations arising in the theory of airfoils

摘要

In this paper, a new efficient and applicable method in order to solve the first kind Cauchy integral equation is presented. For this purpose, this integral equation is converted to the second kind, then the homotopy analysis method is applied to solve the obtained integral equation. Also, the convergence of the proposed method is proved. Several applicable examples are presented which are appeared in the theory of airfoils in fluid mechanics. By plotting the $hbar$-curves, we show the convergence region of the examples and the tables of absolute errors for different values of $hbar$ and $x$ are tabulated.