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Article: Gauss-Jacobi-type quadrature rules for fractional directional integrals

TitleGauss-Jacobi-type quadrature rules for fractional directional integrals
Authors
KeywordsFractional directional integral
Directional derivative
Gauss–Jacobi–Lobatto
Quadrature
Fractional Laplacian
Issue Date2013
PublisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa
Citation
Computers & Mathematics with Applications, 2013, v. 66 n. 5, p. 597-607 How to Cite?
AbstractFractional directional integrals are the extensions of the Riemann–Liouville fractional integrals from one- to multi-dimensional spaces and play an important role in extending the fractional differentiation to diverse applications. In numerical evaluation of these integrals, the weakly singular kernels often fail the conventional quadrature rules such as Newton–Cotes and Gauss–Legendre rules. It is noted that these kernels after simple transforms can be taken as the Jacobi weight functions which are related to the weight factors of Gauss–Jacobi and Gauss–Jacobi–Lobatto rules. These rules can evaluate the fractional integrals at high accuracy. Comparisons with the three typical adaptive quadrature rules are presented to illustrate the efficacy of the Gauss–Jacobi-type rules in handling weakly singular kernels of different strengths. Potential applications of the proposed rules in formulating and benchmarking new numerical schemes for generalized fractional diffusion problems are briefly discussed in the final remarking section.
Persistent Identifierhttp://hdl.handle.net/10722/191158
ISSN
2015 Impact Factor: 1.398
2015 SCImago Journal Rankings: 1.092
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorPang, G-
dc.contributor.authorChen, W-
dc.contributor.authorSze, KY-
dc.date.accessioned2013-09-18T07:16:16Z-
dc.date.available2013-09-18T07:16:16Z-
dc.date.issued2013-
dc.identifier.citationComputers & Mathematics with Applications, 2013, v. 66 n. 5, p. 597-607-
dc.identifier.issn0898-1221-
dc.identifier.urihttp://hdl.handle.net/10722/191158-
dc.description.abstractFractional directional integrals are the extensions of the Riemann–Liouville fractional integrals from one- to multi-dimensional spaces and play an important role in extending the fractional differentiation to diverse applications. In numerical evaluation of these integrals, the weakly singular kernels often fail the conventional quadrature rules such as Newton–Cotes and Gauss–Legendre rules. It is noted that these kernels after simple transforms can be taken as the Jacobi weight functions which are related to the weight factors of Gauss–Jacobi and Gauss–Jacobi–Lobatto rules. These rules can evaluate the fractional integrals at high accuracy. Comparisons with the three typical adaptive quadrature rules are presented to illustrate the efficacy of the Gauss–Jacobi-type rules in handling weakly singular kernels of different strengths. Potential applications of the proposed rules in formulating and benchmarking new numerical schemes for generalized fractional diffusion problems are briefly discussed in the final remarking section.-
dc.languageeng-
dc.publisherPergamon. The Journal's web site is located at http://www.elsevier.com/locate/camwa-
dc.relation.ispartofComputers & Mathematics with Applications-
dc.rightsNOTICE: this is the author’s version of a work that was accepted for publication in Computers & Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, 2013, v. 66 n. 5, p. 597–607. DOI: 10.1016/j.camwa.2013.04.020-
dc.rightsCreative Commons: Attribution 3.0 Hong Kong License-
dc.subjectFractional directional integral-
dc.subjectDirectional derivative-
dc.subjectGauss–Jacobi–Lobatto-
dc.subjectQuadrature-
dc.subjectFractional Laplacian-
dc.titleGauss-Jacobi-type quadrature rules for fractional directional integralsen_US
dc.typeArticleen_US
dc.identifier.emailSze, KY: kysze@hku.hk-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.camwa.2013.04.020-
dc.identifier.scopuseid_2-s2.0-84881478914-
dc.identifier.hkuros231279-
dc.identifier.volume66-
dc.identifier.issue5-
dc.identifier.spage597-
dc.identifier.epage607-
dc.identifier.isiWOS:000323869000004-
dc.publisher.placeUnited Kingdom-

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