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Section B

A pseudo-spectral scheme for the approximate solution of a time-fractional diffusion equation

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Pages 980-994 | Received 09 Jan 2014, Accepted 12 Apr 2014, Published online: 22 May 2014
 

Abstract

We consider an initial-boundary-value problem for a time-fractional diffusion equation with initial condition u0(x) and homogeneous Dirichlet boundary conditions in a bounded interval [0, L]. We study a semidiscrete approximation scheme based on the pseudo-spectral method on Chebyshev–Gauss–Lobatto nodes. In order to preserve the high accuracy of the spectral approximation we use an approach based on the evaluation of the Mittag-Leffler function on matrix arguments for the integration along the time variable. Some examples are presented and numerical experiments illustrate the effectiveness of the proposed approach.

2010 AMS Subject Classification::

Acknowledgements

The work of R.Garrappa has been supported under the GNCS - INdAM Project 2014.

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