Fibonacci-regularization method for solving Cauchy integral equations of the first kind

• Main Authors: Mohammad Ali Fariborzi Araghi, Samad Noeiaghdam
• Format: Article
• Language: English
• Published: Elsevier 2017-09-01
• Series: Ain Shams Engineering Journal
• Subjects: Collocation method; Fibonacci polynomials; Regularization method; First kind Cauchy integral equation
• Online Access: http://www.sciencedirect.com/science/article/pii/S2090447915001525

In this paper, a novel scheme is proposed to solve the first kind Cauchy integral equation over a finite interval. For this purpose, the regularization method is considered. Then, the collocation method with Fibonacci base function is applied to solve the obtained second kind singular integral equation. Also, the error estimate of the proposed scheme is discussed. Finally, some sample Cauchy integral equations stem from the theory of airfoils in fluid mechanics are presented and solved to illustrate the importance and applicability of the given algorithm. The tables in the examples show the efficiency of the method.