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A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo–Fabrizio Derivative

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Abstract

In this paper, we consider numerical solutions of fractional ordinary differential equations with the Caputo–Fabrizio derivative, and construct and analyze a high-order time-stepping scheme for this equation. The proposed method makes use of quadratic interpolation function in sub-intervals, which allows to produce fourth-order convergence. A rigorous stability and convergence analysis of the proposed scheme is given. A series of numerical examples are presented to validate the theoretical claims. Traditionally a scheme having fourth-order convergence could only be obtained by using block-by-block technique. The advantage of our scheme is that the solution can be obtained step by step, which is cheaper than a block-by-block-based approach.

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Authors and Affiliations

  1. School of Data Science and Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

    Junying Cao & Ziqiang Wang

  2. School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High Performance Scientific Computing, Xiamen University, Xiamen, 361005, China

    Chuanju Xu

Authors
  1. Junying Cao
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  2. Ziqiang Wang
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  3. Chuanju Xu
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Correspondence to Chuanju Xu.

Additional information

This research was supported by the National Natural Science Foundation of China (Grant numbers 11501140, 51661135011, 11421110001, and 91630204) and the Foundation of Guizhou Science and Technology Department (No. [2017]1086). The first author would like to acknowledge the financial support by the China Scholarship Council (201708525037).

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Cao, J., Wang, Z. & Xu, C. A High-Order Scheme for Fractional Ordinary Differential Equations with the Caputo–Fabrizio Derivative. Commun. Appl. Math. Comput. 2, 179–199 (2020). https://doi.org/10.1007/s42967-019-00043-8

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  • DOI: https://doi.org/10.1007/s42967-019-00043-8

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