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Multistep collocation methods for integral-algebraic equations with non-vanishing delays

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  • Darania, P.
  • Pishbin, S.

Abstract

In this article, we study the piecewise multistep collocation method for a class of functional integral equations with non-vanishing delays. Based on the notions of the tractability index and the ν-smoothing property of a Volterra integral operator, our numerical analysis and optimal convergence properties are investigated. Here, multistep collocation method which depends on the numerical solution in a fixed number of previous time steps is described by the constructive technique and dividing the definition domain into several subintervals according to the primary discontinuous points associated with the delay function. Numerical experiments confirm the theoretical expectations.

Suggested Citation

  • Darania, P. & Pishbin, S., 2023. "Multistep collocation methods for integral-algebraic equations with non-vanishing delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 33-61.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:33-61
    DOI: 10.1016/j.matcom.2022.08.018
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    References listed on IDEAS

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    1. Balakumar, V. & Murugesan, K., 2015. "Numerical solution of Volterra integral-algebraic equations using block pulse functions," Applied Mathematics and Computation, Elsevier, vol. 263(C), pages 165-170.
    2. Pishbin, S., 2018. "The numerical solution of the semi-explicit IDAEs by discontinuous piecewise polynomial approximation," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 93-104.
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    Cited by:

    1. Bagomghaleh, Shadi Malek & Pishbin, Saeed & Gholami, Gholamhossein, 2024. "Numerical and analytical findings on the Volterra integral-algebraic index-1 system with vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 466(C).

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    2. Bagomghaleh, Shadi Malek & Pishbin, Saeed & Gholami, Gholamhossein, 2024. "Numerical and analytical findings on the Volterra integral-algebraic index-1 system with vanishing delays," Applied Mathematics and Computation, Elsevier, vol. 466(C).

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