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Published Online: 20 October 2016

Introducing graded meshes in the numerical approximation of distributed-order diffusion equations

AIP Conference Proceedings 1776, 070002 (2016); https://doi.org/10.1063/1.4965348
M. L. Morgado1, b) and M. Rebelo2, a)
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Abstract
In this paper we deal with the numerical approximation of initial-boundary value problems to the diffusion equation with distributed order in time. As it is widely known, the solutions of fractional differential equations may present a singularity at t = 0 and therefore in these cases, standard finite difference schemes usually suffer a convergence order reduction with respect to time discretization. In order to overcome this, here we propose a finite difference scheme with a graded time mesh, constructed in such a way that the time step-size is smaller near the potential singular point. Numerical results are presented and compared with those obtained with finite difference schemes with uniform meshes.

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  9. Published by AIP Publishing.

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