# Solving Abel’s equations with the shifted Legendre polynomials

Document Type : Research Paper

Authors

Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.

Abstract

In this article, a numerical method is presented to solve Abel’s equations. In the given method, the solution of the equation is found as a finite expansion of the shifted Legendre polynomials. To this end, the integral and differential parts of the equation are converted to vector-matrix representations. Therefore, the equation is converted to an algebraic system of the equations and by solving it, the solution of the equation is obtained. Further, the numerical example is given to illustrate the method’s efficiency.

Keywords

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### History

• Receive Date: 29 July 2022
• Revise Date: 28 January 2023
• Accept Date: 25 February 2023