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)
-
Details in the research portal "Research@Leibniz University"