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Asymptotic stability of block boundary value methods for delay differential-algebraic equations

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  • Zhang, Chengjian
  • Chen, Hao

Abstract

Block boundary value methods are applied to solve a class of delay differential-algebraic equations. We focus on the asymptotic stability of the numerical methods for linear delay differential-algebraic equations with multiple delays. It is shown that A-stable block boundary value methods satisfying a restrictive condition can preserve the asymptotic stability of the analytical solution. Numerical experiments further confirm the effectiveness and stability of the methods.

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  • 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.
    • Handle: RePEc:eee:matcom:v:81:y:2010:i:1:p:100-108
    DOI: 10.1016/j.matcom.2010.07.012
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    References listed on IDEAS

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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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    1. Chen, Hao & Huang, Qiuyue, 2020. "Kronecker product based preconditioners for boundary value method discretizations of space fractional diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 170(C), pages 316-331.
    2. 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).
    3. 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.
    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.
    5. Zhao, Jingjun & Jiang, Xingzhou & Xu, Yang, 2021. "Convergence of block boundary value methods for solving delay differential algebraic equations with index-1 and index-2," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    6. 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).

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