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Solving nonlinear functional–differential and functional equations with constant delay via block boundary value methods

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  • Yan, Xiaoqiang
  • Zhang, Chengjian

Abstract

This paper deals with the numerical solutions of nonlinear functional-differential and functional equations (FDFEs) with constant delay. The block boundary value methods (BBVMs) are extended to solve the FDFEs. Under the suitable conditions, it is shown that the extended BBVMs are uniquely solvable and globally stable. Moreover, the method can be convergent of order p whenever the Lipschitz condition holds and this method is preconsistent and p-order consistent. With several numerical examples, the theoretical results and computational validity of the extended BBVMs are further confirmed.

Suggested Citation

  • Yan, Xiaoqiang & Zhang, Chengjian, 2019. "Solving nonlinear functional–differential and functional equations with constant delay via block boundary value methods," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 21-32.
    • Handle: RePEc:eee:matcom:v:166:y:2019:i:c:p:21-32
    DOI: 10.1016/j.matcom.2019.04.004
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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.
    2. Bellen, Alfredo & Zennaro, Marino, 2003. "Numerical Methods for Delay Differential Equations," OUP Catalogue, Oxford University Press, number 9780198506546.
    3. Yuexin Yu & Zhongyan Liu & Liping Wen, 2014. "Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-9, May.
    4. Wang, Huiru & Zhang, Chengjian & Zhou, Yongtao, 2018. "A class of compact boundary value methods applied to semi-linear reaction–diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 325(C), pages 69-81.
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    Cited by:

    1. Kumar, Surendra & Sharma, Abhishek & Pal Singh, Harendra, 2021. "Convergence and global stability analysis of fractional delay block boundary value methods for fractional differential equations with delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. Zhou, Quan & Wang, Yinkun & Liu, Yicheng, 2024. "Chebyshev–Picard iteration methods for solving delay differential equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 217(C), pages 1-20.

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