The Fibonacci polynomials solution for Abel’s integral equation of second kind

• Main Author: Haman Deilami Azodi
• Format: Article
• Language: English
• Published: Ferdowsi University of Mashhad 2020-04-01
• Series: Iranian Journal of Numerical Analysis and Optimization
• Subjects: abel’s integral equation; fibonacci polynomials; collocation points; error analysis
• Online Access: https://ijnao.um.ac.ir/article_25138_f3bf154722cfcad2d6a95d1a2c262e8d.pdf

We suggest a convenient method based on the Fibonacci polynomials and the collocation points for solving approximately the Abel’s integral equation of second kind. Initially, the solution is supposed in the form of the Fibonacci polynomials truncated series with the unknown coefficients. Then, by placing this series into the main problem and collocating the resulting equation at some points, a system of algebraic equations is obtained. After solving it, the unknown coefficients and so the solution of main problem are determined. The error analysis is discussed elaborately. Also, the reliability of the method is quantified through numerical examples.