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Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations

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  • Qin, Tingting
  • Zhang, Chengjian

Abstract

This paper deals with stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations (FIDEs). A type of extended one-leg methods are suggested for the FIDEs. The (weak) global stability results of the methods are presented. In particular, it is shown under suitable condition that a G-stable extended BDF method is globally and asymptotically stable for the problems of class FID(α,β,γ,η,+∞). Numerical experiments further illustrate the theoretical results and the methodical effectiveness. In the end, a connection and comparison between the obtained results and the existed ones is given.

Suggested Citation

  • Qin, Tingting & Zhang, Chengjian, 2015. "Stable solutions of one-leg methods for a class of nonlinear functional-integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 47-57.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:47-57
    DOI: 10.1016/j.amc.2014.11.003
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    1. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
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    Cited by:

    1. Wen, Liping & Yu, Yuexin, 2016. "Convergence of Runge–Kutta methods for neutral delay integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 84-96.
    2. Tan, Zengqiang & Zhang, Chengjian, 2018. "Implicit-explicit one-leg methods for nonlinear stiff neutral equations," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 196-210.
    3. Liping Wen & Xiong Liu & Yuexin Yu, 2015. "Stability of Runge-Kutta Methods for Neutral Delay Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2015, pages 1-8, November.
    4. Zhou, Yongtao & Zhang, Chengjian, 2019. "One-leg methods for nonlinear stiff fractional differential equations with Caputo derivatives," Applied Mathematics and Computation, Elsevier, vol. 348(C), pages 594-608.

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