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arXiv · 1507.05706

Numerical solution of the time-fractional Fokker-Planck equation with general forcing

Kim Ngan Le·William McLean·Kassem Mustapha
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Abstract

We study two schemes for a time-fractional Fokker-Planck equation with space- and time-dependent forcing in one space dimension. The first scheme is continuous in time and is discretized in space using a piecewise-linear Galerkin finite element method. The second is continuous in space and employs a time-stepping procedure similar to the classical implicit Euler method. We show that the space discretization is second-order accurate in the spatial $L_2$-norm, uniformly in time, whereas the corresponding error for the time-stepping scheme is $O(k^\alpha)$ for a uniform time step $k$, where $\alpha\in(1/2,1)$ is the fractional diffusion parameter. In numerical experiments using a combined, fully-discrete method, we observe convergence behaviour consistent with these results.

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Kim Ngan Le, William McLean, Kassem Mustapha. 2015-07-21. Numerical solution of the time-fractional Fokker-Planck equation with general forcing. https://doi.org/10.1137/15m1031734

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