An efficient localized collocation solver for anomalous diffusion on surfaces

authored by
Zhuochao Tang, Zhuojia Fu, Hongguang Sun, Xiaoting Liu
Abstract

This paper introduces an efficient collocation solver, the generalized finite difference method (GFDM) combined with the recent-developed scale-dependent time stepping method (SD-TSM), to predict the anomalous diffusion behavior on surfaces governed by surface time-fractional diffusion equations. In the proposed solver, the GFDM is used in spatial discretization and SD-TSM is used in temporal discretization. Based on the moving least square theorem and Taylor series, the GFDM introduces the stencil selection algorithms to choose the stencil support of a certain node from the whole discretization nodes on the surface. It inherits the similar properties from the standard FDM and avoids the mesh generation, which is available particularly for high-dimensional irregular discretization nodes. The SD-TSM is a non-uniform temporal discretization method involving the idea of metric, which links the fractional derivative order with the non-uniform discretization strategy. Compared with the traditional time stepping methods, GFDM combined with SD-TSM deals well with the low accuracy in the early period. Numerical investigations are presented to demonstrate the efficiency and accuracy of the proposed GFDM in conjunction with SD-TSM for solving either single or coupled fractional diffusion equations on surfaces.

Organisation(s)
Institute of Continuum Mechanics
External Organisation(s)
Hohai University
Nanjing University of Aeronautics and Astronautics
Type
Article
Journal
Fractional Calculus and Applied Analysis
Volume
24
Pages
865-894
No. of pages
30
ISSN
1311-0454
Publication date
06.2021
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Analysis, Applied Mathematics
Electronic version(s)
https://doi.org/10.1515/fca-2021-0037 (Access: Closed)
 

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