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Journal of Scientific Computing

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03-06-2016

A Weighted ADI Scheme for Subdiffusion Equations

Authors: Hong-lin Liao, Ying Zhao, Xing-hu Teng

Published in: Journal of Scientific Computing | Issue 3/2016

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Abstract

A weighted ADI scheme is proposed for solving two-dimensional anomalous diffusion equations with the fractional Caputo derivative. The Alikhanov formula (J Comput Phys 280:424–438, 2015) with a weaker assumption is applied to approximate the fractional derivative and a high-order perturbed term of temporal order \(1+2\alpha \) is added to the pure implicit approach. By using the discrete energy method, it is proven that the ADI scheme is stable and convergent with the temporal order of \(\min \{1+2\alpha ,2\}\) such that it achieves second-order time accuracy when \(\frac{1}{2}\le \alpha <1\). Numerical experiments are included to support the theoretical analysis. Application of suggested method to the solution which lacks the smoothness near the initial time is examined by employing a class of nonuniform meshes refined near the singular point.

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Title: A Weighted ADI Scheme for Subdiffusion Equations
Authors: Hong-lin Liao
Ying Zhao
Xing-hu Teng
Publication date: 03-06-2016
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 3/2016
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-016-0230-9

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