Analysis and Efficient Implementation of Quadratic Spline Collocation ADI Methods for Variable-Order Time-Fractional Mobile-Immobile Diffusion Equations
Year: 2025
Author: Jun Liu, Hongfei Fu, Bingyin Zhang, Jiansong Zhang
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 226–258
Abstract
In this paper, a quadratic spline collocation (QSC) method combined with L1 time discretization in the framework of alternating direction implicit (ADI) approach, namely ADI-QSC-L1 method, is developed to solve the variable-order time-fractional mobile-immobile diffusion equations in multi-dimensional spaces. Discrete L2 norm-based stability and error estimate are carefully discussed, which show that the proposed method is unconditionally stable and convergent with first-order accuracy in time and second-order accuracy in space. Then, based on the exponential-sum-approximation technique for the fast evaluation of the variable-order Caputo fractional derivative, an efficient implementation strategy of the ADI-QSC-L1 method, named ADI-QSC-FL1 is presented, which further improves the computational efficiency by reduced memory requirement and computational cost. Finally, numerical examples are provided to support both the theoretical results and efficiency of the developed method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2024-0086
Numerical Mathematics: Theory, Methods and Applications, Vol. 18 (2025), Iss. 1 : pp. 226–258
Published online: 2025-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 33
Keywords: Time-fractional mobile-immobile diffusion equations variable-order QSC method ADI stability and convergence fast implementation.