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

Kim Ngan Le, William McLean, Kassem Mustapha

Research output: Contribution to journalArticleResearchpeer-review

27 Citations (Scopus)

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 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, uniformly in time, whereas the corresponding error for the time-stepping scheme is O(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 behavior consistent with these results.

Original languageEnglish
Pages (from-to)1763-1784
Number of pages22
JournalSIAM Journal on Numerical Analysis
Volume54
Issue number3
DOIs
Publication statusPublished - 1 Jan 2016
Externally publishedYes

Keywords

  • Finite elements
  • Fractional diffusion
  • Gronwall inequality
  • Stability
  • Time-dependent forcing

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