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The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for Solving the Time Multi-term and Distributed-Order Fractional Sub-diffusion Equations

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Abstract

In this article, a special point is found for the interpolation approximation of the linear combination of multi-term fractional derivatives. The derived numerical differentiation formula can achieve at least second order accuracy. Then the formula is used to numerically solve the time multi-term and distributed-order fractional sub-diffusion equations. Several unconditionally stable and convergent difference schemes are presented. The stability and convergence of the difference schemes are discussed. Some numerical examples are provided to show the efficiency of the proposed difference schemes.

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Acknowledgements

The authors would like to deeply thank two anonymous reviewers for their constructive comments and suggestions to greatly improve this work.

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Authors and Affiliations

  1. College of Science, Nanjing University of Posts and Telecommunications, Nanjing, 210023, People’s Republic of China

    Guang-hua Gao

  2. Institute of Applied Mathematics and Automation, Russian Academy of Sciences, Ul. Shortanova 89 a, Nalchik, 360000, Russia

    Anatoly A. Alikhanov

  3. School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Zhi-zhong Sun

Authors
  1. Guang-hua Gao
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  2. Anatoly A. Alikhanov
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  3. Zhi-zhong Sun
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Corresponding author

Correspondence to Zhi-zhong Sun.

Additional information

The research is supported by the National Natural Science Foundation of China (Grant Nos. 11401319, 11671081) and by the Russian Presidential Grant for young scientists (Grant No. MK-3360.2015.1) and by 1311 talent program from Nanjing University of Posts and Telecommunications.

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Gao, Gh., Alikhanov, A.A. & Sun, Zz. The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for Solving the Time Multi-term and Distributed-Order Fractional Sub-diffusion Equations. J Sci Comput 73, 93–121 (2017). https://doi.org/10.1007/s10915-017-0407-x

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  • DOI: https://doi.org/10.1007/s10915-017-0407-x

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