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Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications

Monteghetti, Florian and Matignon, Denis and Piot, Estelle Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications. ( In Press: 2018) Applied Numerical Mathematics. ISSN 0168-9274

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Official URL: https://doi.org/10.1016/j.apnum.2018.12.003

Abstract

This paper investigates the time-local discretization, using Gaussian quadrature, of a class of diffusive operators that includes fractional operators, for application in fractional differential equations and related eigenvalue problems. A discretization based on the Gauss–Legendre quadrature rule is analyzed both theoretically and numerically. Numerical comparisons with both optimization-based and quadrature-based methods highlight its applicability. In addition, it is shown, on the example of a fractional delay differential equation, that quadrature-based discretization methods are spectrally correct, i.e. that they yield an unpolluted and convergent approximation of the essential spectrum linked to the fractional derivative, by contrast with optimization-based methods that can yield polluted spectra whose convergence is difficult to assess.

Item Type:Article
Audience (journal):International peer-reviewed journal
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Institution:Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
French research institutions > Office National d'Etudes et Recherches Aérospatiales - ONERA (FRANCE)
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This research has been financially supported by the French ministry of defense (Direction Générale de l’Armement) and ONERA (the French Aerospace Lab).
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Deposited By: Denis Matignon
Deposited On:29 Jan 2019 09:36

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