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Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations

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Abstract

This paper deals with the blow-up behavior of numerical solutions to nonlinear fractional ordinary differential equations with a dissipative term. Based on the positivity preservation of the explicit L1-scheme, it is shown that for sufficiently small initial values, numerical solutions exist globally. Whereas for large initial values, numerical solutions with a suitable adaptive step strategy blow up in finite time. Finally, some numerical experiments are provided for verifying the theoretical analysis.

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Funding

This research was supported by the National Natural Science Foundation of China (NSFC 11771128 and NSFC 11871179).

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Authors and Affiliations

  1. School of Applied Mathematics, Guangdong University of Technology, 510006, Guangzhou, China

    Qi Wang

  2. School of Mathematics, Harbin Institute of Technology, Harbin, China

    Zhanwen Yang

  3. Beijing Computational Science Research Center, 100193, Beijing, China

    Chengchao Zhao

Authors
  1. Qi Wang
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  2. Zhanwen Yang
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  3. Chengchao Zhao
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Correspondence to Zhanwen Yang.

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Wang, Q., Yang, Z. & Zhao, C. Numerical blow-up analysis of the explicit L1-scheme for fractional ordinary differential equations. Numer Algor 89, 451–463 (2022). https://doi.org/10.1007/s11075-021-01121-w

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