The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation / Pezza, L.; Pitolli, F.. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 9:1(2018), pp. 104-120. [10.1515/caim-2018-0007]

A fractional spline collocation-Galerkin method for the time-fractional diffusion equation

Pezza, L.;Pitolli, F.
2018

Abstract

The aim of this paper is to numerically solve a diffusion differential problem having time derivative of fractional order. To this end we propose a collocation-Galerkin method that uses the fractional splines as approximating functions. The main advantage is in that the derivatives of integer and fractional order of the fractional splines can be expressed in a closed form that involves just the generalized finite difference operator. This allows us to construct an accurate and efficient numerical method. Several numerical tests showing the effectiveness of the proposed method are presented.
2018
collocation method; fractional diffusion problem; fractional spline; Galerkin method;
01 Pubblicazione su rivista::01a Articolo in rivista
A fractional spline collocation-Galerkin method for the time-fractional diffusion equation / Pezza, L.; Pitolli, F.. - In: COMMUNICATIONS IN APPLIED AND INDUSTRIAL MATHEMATICS. - ISSN 2038-0909. - 9:1(2018), pp. 104-120. [10.1515/caim-2018-0007]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1184511
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