Solving anisotropic subdiffusion problems in annuli and shells

• Published in: Journal of computational and applied mathematics Vol. 401; p. 113764
• Main Authors: Tan, Jinying, Liu, Jiangguo
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2022
• Subjects: Anisotropy; Caputo time-fractional derivative; Chebyshev differentiation matrices; Polar, cylindrical, and spherical coordinates; Spectral collocation; Subdiffusion; Polar, cylindrical, and spherical coordinates; Chebyshev differentiation matrices; Anisotropy; Spectral collocation; Caputo time-fractional derivative; Subdiffusion
• ISSN: 0377-0427; 1879-1778
• DOI: 10.1016/j.cam.2021.113764

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.