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The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for the Time Multi-term Fractional Wave Equation

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Abstract

In this paper, two temporal second-order schemes are derived and analyzed for the time multi-term fractional diffusion-wave equation based on the order reduction technique. The weighted average at two time levels is applied to the discretization of the spatial derivative, in which the weight coefficient corresponds to the optimal point for the time discretization. The two difference schemes are proved to be uniquely solvable. The stability and convergence are rigorously investigated utilizing the energy method. In addition, a fast difference scheme is also presented. The applicability and the accuracy of the schemes are demonstrated by several numerical experiments.

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Authors and Affiliations

  1. Department of Mathematics and Physics, Nanjing Institute of Technology, Nanjing, 211167, People’s Republic of China

    Hong Sun

  2. The Jiangsu Provincial Key Laboratory of Networked Collective Intelligence, School of Mathematics, Southeast University, Nanjing, 210096, People’s Republic of China

    Xuan Zhao

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

    Zhi-zhong Sun

Authors
  1. Hong Sun
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  2. Xuan Zhao
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  3. Zhi-zhong Sun
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Correspondence to Zhi-zhong Sun.

Additional information

The research is supported by the National Natural Science Foundation of China (Grant Nos. 11671081, 11701229, 11701081), Natural Science Youth Foundation of Jiangsu Province (Nos. BK20170567, BK20160660) and the Fundamental Research Funds for the Central Universities (No. 2242016K41029), the Jiangsu Provincial Key Laboratory of Networked Collective Intelligence (No. BM2017002).

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Sun, H., Zhao, X. & Sun, Zz. The Temporal Second Order Difference Schemes Based on the Interpolation Approximation for the Time Multi-term Fractional Wave Equation. J Sci Comput 78, 467–498 (2019). https://doi.org/10.1007/s10915-018-0820-9

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  • DOI: https://doi.org/10.1007/s10915-018-0820-9

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