University of TabrizComputational Methods for Differential Equations2345-398211420230701Solving Abel’s equations with the shifted Legendre polynomials8658751597510.22034/cmde.2023.52786.2222ENMaryamShahsavariDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.LeilaTorkzadehDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.0000-0002-2504-4048KazemNouriDepartment of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.0000-0002-7922-5848Journal Article20220729In 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