A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system

Liu, Xiaoting1,2; Zhang, Yong3; Sun, HongGuang1,4; Guo, Zhilin5

2021-10-01

10.1007/s00466-021-02085-3

COMPUTATIONAL MECHANICS   影响因子和分区

0178-7675

1432-0924

The impulsive differential equations are regarded as an optimal method to describe solute concentration fluctuation transport in unsteady flow field which are influenced by natural factors or human activities. The key difficulty of impulsive fractional-order system (IFS) in numerical discretization is that fractional-orders are different in different impulsive period. This paper proposes a double-scale-dependent mesh method considering the period memory, and makes a comparison with four collocation modes for the implict difference method. Furthermore, the stability and truncation error for graded meshes are estimated and analyzed. The analysis result reveals that the convergence rate mainly depends on the largest fractional order on the IFS. Numerical results show all graded meshes (producing the dense mesh at the early stage) provide better performance than uniform mesh. Meanwhile, the PDE cases show double-scale-dependent mesh is the most efficient numerical approximation method for the pulsation diffusion of contaminant in porous medium.

Unsteady flow field Impulsive fractional-order system Double-scale-dependent mesh Graded mesh Computational efficiency

SCI ; EI

英语

其他

National Natural Science Foundation of China[11972148,41831289,41931292] ; Natural Science Foundation of Jiangsu Province[BK20190024]

Mathematics ; Mechanics

Mathematics, Interdisciplinary Applications ; Mechanics

WOS:000706000100001

SPRINGER

20214111013095

Algebra ; Computational efficiency ; Differential equations ; Flow fields ; Numerical methods ; Porous materials ; Unsteady flow

Fluid Flow, General:631.1 ; Computer Applications:723.5 ; Algebra:921.1 ; Calculus:921.2 ; Combinatorial Mathematics, Includes Graph Theory, Set Theory:921.4 ; Numerical Methods:921.6 ; Materials Science:951

ENGINEERING

Web of Science

1.Hohai Univ, State Key Lab Hydrol Water Resources & Hydraul En, Nanjing 210098, Jiangsu, Peoples R China
2.Three Gorges Corp, Beijing 100038, Peoples R China
3.Univ Alabama, Dept Geol Sci, Tuscaloosa, AL 35487 USA
4.Hohai Univ, Coll Mech & Mat, Inst Soft Matter Mech, Nanjing 210098, Jiangsu, Peoples R China
5.Southern Univ Sci & Technol, Sch Environm Sci & Engn, Shenzhen 518055, Peoples R China

Liu, Xiaoting,Zhang, Yong,Sun, HongGuang,et al. A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system[J]. COMPUTATIONAL MECHANICS,2021,69:113-131.

Liu, Xiaoting,Zhang, Yong,Sun, HongGuang,&Guo, Zhilin.(2021).A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system.COMPUTATIONAL MECHANICS,69,113-131.

Liu, Xiaoting,et al."A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system".COMPUTATIONAL MECHANICS 69(2021):113-131.