Title of article
Solving Abel’s equations with the shifted Legendre polynomials
Author/Authors
Shahsavari ، Maryam Department of Mathematics - Faculty of Mathematics, Statistics and Computer Sciences - Semnan University , Torkzadeh ، Leila Department of Mathematics - Faculty of Mathematics, Statistics and Computer Sciences - Semnan University , Nouri ، Kazem Department of Mathematics - Faculty of Mathematics, Statistics and Computer Sciences - Semnan University
From page
865
To page
875
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
Abel’s equation , Integral equation , Caputo differential operator , Shifted Legendre polynomial
Journal title
Computational Methods for Differential Equations
Journal title
Computational Methods for Differential Equations
Record number
2738861
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