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- Title
A fractional-order dependent collocation method with graded mesh for impulsive fractional-order system.
- Authors
Liu, Xiaoting; Zhang, Yong; Sun, HongGuang; Guo, Zhilin
- Abstract
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.
- Subjects
UNSTEADY flow; IMPULSIVE differential equations; POROUS materials; COLLOCATION methods
- Publication
Computational Mechanics, 2022, Vol 69, Issue 1, p113
- ISSN
0178-7675
- Publication type
Article
- DOI
10.1007/s00466-021-02085-3