The Fibonacci polynomials solution for Abel’s integral equation of second kind
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 pl...
Main Author: | |
---|---|
Format: | Article |
Language: | English |
Published: |
Ferdowsi University of Mashhad
2020-04-01
|
Series: | Iranian Journal of Numerical Analysis and Optimization |
Subjects: | |
Online Access: | https://ijnao.um.ac.ir/article_25138_f3bf154722cfcad2d6a95d1a2c262e8d.pdf |
id |
doaj-5f2c16fa1bc347b9b31ef2d651afb96e |
---|---|
record_format |
Article |
spelling |
doaj-5f2c16fa1bc347b9b31ef2d651afb96e2021-02-17T10:41:32ZengFerdowsi University of MashhadIranian Journal of Numerical Analysis and Optimization2423-69772423-69692020-04-01101637910.22067/ijnao.v10i1.8182825138The Fibonacci polynomials solution for Abel’s integral equation of second kindHaman Deilami Azodi0Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.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.https://ijnao.um.ac.ir/article_25138_f3bf154722cfcad2d6a95d1a2c262e8d.pdfabel’s integral equationfibonacci polynomialscollocation pointserror analysis |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Haman Deilami Azodi |
spellingShingle |
Haman Deilami Azodi The Fibonacci polynomials solution for Abel’s integral equation of second kind Iranian Journal of Numerical Analysis and Optimization abel’s integral equation fibonacci polynomials collocation points error analysis |
author_facet |
Haman Deilami Azodi |
author_sort |
Haman Deilami Azodi |
title |
The Fibonacci polynomials solution for Abel’s integral equation of second kind |
title_short |
The Fibonacci polynomials solution for Abel’s integral equation of second kind |
title_full |
The Fibonacci polynomials solution for Abel’s integral equation of second kind |
title_fullStr |
The Fibonacci polynomials solution for Abel’s integral equation of second kind |
title_full_unstemmed |
The Fibonacci polynomials solution for Abel’s integral equation of second kind |
title_sort |
fibonacci polynomials solution for abel’s integral equation of second kind |
publisher |
Ferdowsi University of Mashhad |
series |
Iranian Journal of Numerical Analysis and Optimization |
issn |
2423-6977 2423-6969 |
publishDate |
2020-04-01 |
description |
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. |
topic |
abel’s integral equation fibonacci polynomials collocation points error analysis |
url |
https://ijnao.um.ac.ir/article_25138_f3bf154722cfcad2d6a95d1a2c262e8d.pdf |
work_keys_str_mv |
AT hamandeilamiazodi thefibonaccipolynomialssolutionforabelsintegralequationofsecondkind AT hamandeilamiazodi fibonaccipolynomialssolutionforabelsintegralequationofsecondkind |
_version_ |
1724265342182621184 |