Efficient Numerical Solution of Space-Fractional Diffusion Problems

Izsák, Ferenc and Szekeres, Béla (2019) Efficient Numerical Solution of Space-Fractional Diffusion Problems. In: Progress in Industrial Mathematics at ECMI 2018. Springer Nature Switzerland AG, pp. 307-312. ISBN 978-3-030-27550-1

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Abstract

An efficient numerical method is introduced for the solution of space-fractional diffusion problems. We use the spectral fractional Laplacian operator with homogeneous Neumann and Dirichlet boundary conditions. The spatial discretization is based on the matrix transformation method. Using a recent algorithm for the computation of fractional matrix power-vector products and explicit time stepping, we develop a simple and efficient full discretization. The performance of our approach is demonstrated in some numerical experiments.

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