Solving anisotropic subdiffusion problems in annuli and shells

This paper presents a family of numerical solvers for anisotropic subdiffusion problems in annuli and also cylindrical and spherical shells. The fractional order Caputo temporal derivative is discretized based on linear interpolation. The spatial Laplacian is discretized by utilizing Chebyshev and F...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2022-02, Vol.401, p.113764, Article 113764
Main Authors: Tan, Jinying, Liu, Jiangguo
Format: Article
Language:English
Subjects:
Anisotropy
Caputo time-fractional derivative
Chebyshev differentiation matrices
Polar, cylindrical, and spherical coordinates
Spectral collocation
Subdiffusion
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Summary:This paper presents a family of numerical solvers for anisotropic subdiffusion problems in annuli and also cylindrical and spherical shells. The fractional order Caputo temporal derivative is discretized based on linear interpolation. The spatial Laplacian is discretized by utilizing Chebyshev and Fourier spectral collocation. Detailed discussion and useful formulas are presented for polar, cylindrical, and spherical coordinate systems. Numerical experiments along with a brief analysis are presented to demonstrate the accuracy and efficiency of these solvers. These solvers represent a continuation of our work in Tan and Liu (2020) and shall be useful for numerical simulations of subdiffusion problems in cellular cytoplasm and other similar settings.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2021.113764