TY - JOUR

T1 - An efficient localized collocation solver for anomalous diffusion on surfaces

AU - Tang, Zhuochao

AU - Fu, Zhuojia

AU - Sun, Hongguang

AU - Liu, Xiaoting

N1 - Funding Information: The work described in this paper was supported by the National Science Fund of China (Grant Nos. 11772119, 11572111), Alexander von Humboldt Research Fellowship (ID: 1195938), the Foundation for Open Project of State Key Laboratory of Mechanics and Control of Mechanical Structures (Nanjing University of Aeronautics and astronautics) (Grant No. MCMS-E-0519G01) and the Six Talent Peaks Project in Jiangsu Province of China (Grant No. 2019-KTHY-009).

PY - 2021/6

Y1 - 2021/6

N2 - 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.

AB - 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.

KW - 35K57

KW - 65D18

KW - 65M70

KW - Primary 26A33

KW - Secondary 90C32

UR - http://www.scopus.com/inward/record.url?scp=85108870084&partnerID=8YFLogxK

U2 - 10.1515/fca-2021-0037

DO - 10.1515/fca-2021-0037

M3 - Article

AN - SCOPUS:85108870084

VL - 24

SP - 865

EP - 894

JO - Fractional Calculus and Applied Analysis

JF - Fractional Calculus and Applied Analysis

SN - 1311-0454

IS - 3

ER -