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Generalized Störmer-Cowell methods for the nonlinear second-order delay integro-differential equations with initial conditions

Author

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  • Wang, Huiru
  • Zhou, Yongtao
  • Xiong, Wenzhuo
  • Yan, Xiaoqiang

Abstract

In this paper, a kind of adapted numerical methods are constructed to discretize nonlinear second-order integro-differential equations with delay and initial conditions. The approximation methods are developed through a combination of the fundamental generalized Störmer-Cowell methods (GSCMs) and compound quadrature (CQ) formulas. Under several appropriate conditions, we give the criteria on unique solvability, stability and convergence. Moreover, we prove that the resulting numerical methods have the accuracy of min{p,q}, in which p,q, respectively, denotes the GSCMs’ consistence order and the CQ formulas’ convergence order. Numerical experiments are performed to show methods’ computational effectiveness and accuracy. Besides, a comparison is provided among the adapted GSCMs, the adapted implicit Runge-Kutta-Nyström methods and the extended block boundary value methods, which indicates that the constructed methods are comparable.

Suggested Citation

  • Wang, Huiru & Zhou, Yongtao & Xiong, Wenzhuo & Yan, Xiaoqiang, 2026. "Generalized Störmer-Cowell methods for the nonlinear second-order delay integro-differential equations with initial conditions," Applied Mathematics and Computation, Elsevier, vol. 512(C).
    • Handle: RePEc:eee:apmaco:v:512:y:2026:i:c:s0096300325004965
    DOI: 10.1016/j.amc.2025.129771
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    References listed on IDEAS

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    1. T. E. Simos & Jesus Vigo Aguiar, 2000. "A New Modified Runge–Kutta–Nyström Method With Phase-Lag Of Order Infinity For The Numerical Solution Of The Schrödinger Equation And Related Problems," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1195-1208.
    2. Li, Cui & Zhang, Chengjian, 2017. "The extended generalized Störmer–Cowell methods for second-order delay boundary value problems," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 87-95.
    3. Chen, Hao & Yang, Yeru, 2021. "Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems," Applied Mathematics and Computation, Elsevier, vol. 400(C).
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    1. Chen, Hao & Yang, Yeru, 2021. "Generalized Störmer-Cowell methods with efficient iterative solver for large-scale second-order stiff semilinear systems," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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