Solving Abel’s equations with the shifted Legendre polynomials

Shahsavari, Maryam; Torkzadeh, Leila; Nouri, Kazem

doi:10.22034/cmde.2023.52786.2222

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	Solving Abel’s equations with the shifted Legendre polynomials
Computational Methods for Differential Equations
مقاله 15، دوره 11، شماره 4، مهر 2023، صفحه 865-875 اصل مقاله (270.86 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2023.52786.2222
نویسندگان
Maryam Shahsavari؛ Leila Torkzadeh^* ؛ Kazem Nouri
Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, P. O. Box 35195-363, Semnan, Iran.
چکیده
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.
کلیدواژه‌ها
Abel’s equation؛ Integral equation؛ Caputo differential operator؛ Shifted Legendre polynomial

مراجع
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Solving Abel’s equations with the shifted Legendre polynomials