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

Iranian Journal of Numerical Analysis and Optimization

مقاله 5، دوره 10، شماره 1 - شماره پیاپی 17، تیر 2020، صفحه 63-79   

نوع مقاله: Research Article

شناسه دیجیتال (DOI): 10.22067/ijnao.v10i1.81828

نویسنده

H. Deilami Azodi^*

Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

چکیده

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.

کلیدواژه‌ها

Abel’s integral equation؛ Fibonacci polynomials؛ Collocation points؛ error analysis

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