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Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations

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Abstract

A class of modified Du Fort–Frankel-type schemes is investigated for fractional subdiffusion equations in the Jumarie’s modified Riemann–Liouville form with constant, variable or distributed fractional order. New explicit difference methods are constructed by combining the \(L1\) approximation of the modified fractional derivative with the idea of Du Fort–Frankel scheme, well-known for ordinary diffusion equations. Unconditional stability of the explicit methods is established in the sense of a discrete energy norm. The proposed schemes are shown to be convergent under the time-step (consistency) restriction of the classical Du Fort–Frankel scheme. Numerical examples are included to support our theoretical results.

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Authors and Affiliations

  1. Institute of Sciences, PLA University of Science and Technology, Nanjing, 211101, People’s Republic of China

    Hong-lin Liao, Ying Zhao & Han-sheng Shi

  2. School of Mathematical Science, Soochow University, Suzhou, 215006, People’s Republic of China

    Ya-nan Zhang

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  1. Hong-lin Liao
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  2. Ya-nan Zhang
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  3. Ying Zhao
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  4. Han-sheng Shi
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Correspondence to Hong-lin Liao.

Additional information

Hong-lin Liao and Han-sheng Shi are supported by National Science Foundation for Young Scientists of China (No. 11001271, 11201239), and Ya-nan Zhang is supported by National Science Foundation of China (No. 11326229) and China Postdoctoral Science Foundation (2013M530265).

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Liao, Hl., Zhang, Yn., Zhao, Y. et al. Stability and Convergence of Modified Du Fort–Frankel Schemes for Solving Time-Fractional Subdiffusion Equations. J Sci Comput 61, 629–648 (2014). https://doi.org/10.1007/s10915-014-9841-1

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  • DOI: https://doi.org/10.1007/s10915-014-9841-1

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