期刊名称：Journal of Interpolation and Approximation in Scientific Computing
印刷版ISSN：2194-3907
电子版ISSN：2194-3907
出版年度：2016
卷号：2016
期号：1
页码：1-13
DOI：10.5899/2016/jiasc-00092
出版社：ISPACS GmbH
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.
关键词：Theory of airfoils; Homotopy analysis method; Cauchy integral equations of the first kind; $\hbar$-curve
