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A kind of generalized backward differentiation formulae for solving fractional differential equations

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  • Zhao, Jingjun
  • Jiang, Xingzhou
  • Xu, Yang

Abstract

A new kind of numerical method based on generalized backward differentiation formulae is established for solving fractional differential equations. An estimate of the inverse of a class of Toeplitz matrix, which is related to the method, is given. By using the estimate, convergence and stability of the method are analyzed. It is shown that the method has high order of convergence and good stability. Some numerical experiments are also given to illustrate the effectiveness of the method.

Suggested Citation

  • Zhao, Jingjun & Jiang, Xingzhou & Xu, Yang, 2022. "A kind of generalized backward differentiation formulae for solving fractional differential equations," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    • Handle: RePEc:eee:apmaco:v:419:y:2022:i:c:s0096300321009553
    DOI: 10.1016/j.amc.2021.126872
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    References listed on IDEAS

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    1. Zhang, Chengjian & Chen, Hao, 2010. "Asymptotic stability of block boundary value methods for delay differential-algebraic equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(1), pages 100-108.
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    Cited by:

    1. Yang, Changqing, 2023. "Improved spectral deferred correction methods for fractional differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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