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Article Dans Une Revue Applied Numerical Mathematics Année : 2020

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

Résumé

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.
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Dates et versions

hal-02882761 , version 1 (27-06-2020)

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Paternité - Pas d'utilisation commerciale - Pas de modification

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Florian Monteghetti, Denis Matignon, Estelle Piot. Time-local discretization of fractional and related diffusive operators using Gaussian quadrature with applications. Applied Numerical Mathematics, 2020, 155, pp.73-92. ⟨10.1016/j.apnum.2018.12.003⟩. ⟨hal-02882761⟩
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