<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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. </p></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.

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

Communications in Applied and Industrial Mathematics

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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...

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

Publié en ligne: 24 mars 2018

Pages: 104 - 120

Reçu: 12 janv. 2017

Accepté: 27 févr. 2018

DOI: https://doi.org/10.1515/caim-2018-0007

Mots clés
Fractional diffusion problem, Collocation method, Galerkin method, Fractional spline

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Publié en ligne: 24 mars 2018

Pages: 104 - 120

Reçu: 12 janv. 2017

Accepté: 27 févr. 2018

DOI: https://doi.org/10.1515/caim-2018-0007

Mots clésFractional diffusion problem, Collocation method, Galerkin method, Fractional spline

© 2018

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Mots clés
Fractional diffusion problem, Collocation method, Galerkin method, Fractional spline