The finite difference method for Caputo-type parabolic equation with fractional Laplacian: One-dimension case

Ye Hu, Changpin Li and Hefeng Li

Chaos, Solitons & Fractals, 2017, vol. 102, issue C, 319-326

Abstract: In this paper, we present the finite difference method for Caputo-type parabolic equation with fractional Laplacian, where the time derivative is in the sense of Caputo with order in (0, 1) and the spatial derivative is the fractional Laplacian. The Caputo derivative is evaluated by the L1 approximation, and the fractional Laplacian with respect to the space variable is approximated by the Caffarelli–Silvestre extension. The difference schemes are provided together with the convergence and error estimates. Finally, numerical experiments are displayed to verify the theoretical results.

Keywords: Fractional Laplacian; Caputo derivative; Caffarelli–Silvestre extension; Finite difference method; Convergence (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:102:y:2017:i:c:p:319-326

DOI: 10.1016/j.chaos.2017.03.038

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