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Solving Abel's equations with the shifted Legendre polynomials | ||
| Computational Methods for Differential Equations | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 06 اسفند 1401 اصل مقاله (985.13 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 | ||
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آمار تعداد مشاهده مقاله: 41 تعداد دریافت فایل اصل مقاله: 53 |
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