University of Tabriz Computational Methods for Differential Equations 2345-3982 11 4 2023 07 01 Solving Abel’s equations with the shifted Legendre polynomials 865 875 15975 10.22034/cmde.2023.52786.2222 EN Maryam Shahsavari Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran. Leila Torkzadeh Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran. Kazem Nouri Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran. Journal Article 2022 07 29 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. https://cmde.tabrizu.ac.ir/article_15975_cd59407bcfd2b0c8e2fa282de1e91a2a.pdf