An averaged L1-type compact difference method for time-fractional mobile/immobile diffusion equations with weakly singular solutions
APPLIED MATHEMATICS LETTERS(2022)
Abstract
This paper is concerned with a new numerical method for time-fractional mobile/immobile diffusion equations with weakly singular solutions. We propose an averaged L1-type compact difference method, which improves the temporal convergence order of the traditional L1-type method and is also superior to the WSGD-type and L2- 1(sigma)-type methods in terms of regularity requirements. Taking into account the weak singularity of the solution at the initial time, we prove that the proposed method is unconditionally convergent with the convergence order O(tau(2)| ln tau| + h(4)), where tau and h are the sizes of the time and spatial steps, respectively. Numerical results confirm the theoretical convergence result. (c) 2022 Elsevier Ltd. All rights reserved.
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Key words
Time-fractional mobile/immobile diffusion equation,Averaged L1 formula,Compact difference method,High-order convergence
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