A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations

	A new operational matrix of Muntz-Legendre polynomials and Petrov-Galerkin method for solving fractional Volterra-Fredholm integro-differential equations
Computational Methods for Differential Equations
مقاله 1، دوره 8، شماره 3، آبان 2020، صفحه 408-423 اصل مقاله (315.73 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.32623.1515
نویسندگان
Sedigheh Sabermahani؛ Yadollah Ordokhani^*
Department of Mathematics, Faculty of Mathematical Sciences, Alzahra University, Tehran, Iran.
چکیده
This manuscript is devoted to present an efficient numerical method for finding numerical solution of Volterra-Fredholm integro-differential equations of fractional-order. The technique is based on the M\"{u}ntz-Legendre polynomials and Petrov-Galerkin method. A new Riemann-Liouville operational matrix for M\"{u}ntz-Legendre polynomials is proposed using Laplace transform. Employing this operational matrix and Petrov-Galerkin method, the problem transforms to a system of algebraic equations. Next, we solve this system by applying any iterative method. An estimation of the error is proposed. The efficiency and accuracy of the present scheme is illustrated using several examples.
کلیدواژه‌ها
Muntz-Legendre polynomia؛ Petrov-Galerkin method؛ Laplace transform

آمار تعداد مشاهده مقاله: 783 تعداد دریافت فایل اصل مقاله: 847

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