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

Speaker: 

Kim Ngan Le

Affiliation: 

UNSW

Date: 

Tue, 09/02/2016 - 11:30am to 11:55am

Venue: 

RC-2063, The Red Centre, UNSW

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 L2-norm, whereas the corresponding error for the time-stepping scheme is of order kα for a uniform time step k, where α ∈ (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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