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عنوان
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Nonstandard Gauss-Lobatto quadrature approximation to fractional derivatives
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نوع پژوهش
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مقاله چاپشده در مجلات علمی
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کلیدواژهها
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fractional derivative, quadrature rule, Gaussian quadrature, nodes, weights, software implementation, Mathematica package
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چکیده
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A family of nonstandard Gauss-Jacobi-Lobatto quadratures for numerical calculating integrals of the form $\int_{-1}^1 f'(x)(1-x)^\alpha{\D}x$, $\alpha>-1$, is derived and applied to approximation of the usual fractional derivative. A software implementation of such quadratures was done by the recent {\sc Mathematica} package {\tt OrthogonalPolynomials} (cf. [A.S.~Cvetkovi\'c, G.V.~Milovanovi\'c, Facta Univ. Ser. Math. Inform. {\bf19} (2004), 17--36] and [G.V.~Milovanovi\'c, A.S.~Cvetkovi\'c, Math. Balkanica {\bf26} (2012), 169--184]). Several numerical examples are presented and they show the effectiveness of the proposed approach.
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پژوهشگران
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گرادیمیر و. میلووانوویچ (نفر دوم)، شاهرخ اسمعیلی (نفر اول)
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