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A simplified discontinuous reproducing kernel method for impulsive differential equations

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  • Mei, Liangcai
  • Zhang, Yingchao
  • Wu, Boying
  • Lin, Yingzhen

Abstract

In this article, a spatial concept of direct sum space based on the discontinuous reproducing kernel method (RKM for short) is proposed for impulsive differential equations, and a reproducing kernel numerical solution method is constructed. Based on the piecewise smoothness of the solution, a discontinuous reproducing kernel is constructed, and a direct sum space is constructed in vector form to represent the structure of the equation system. Furthermore, the simplified RKM is used to solve the operator equation, and an approximate solution in series form is obtained. Finally, the regularity analysis and uniform convergence analysis are carried out, and numerical experiments verify the second-order convergence and stability of the algorithm.

Suggested Citation

  • Mei, Liangcai & Zhang, Yingchao & Wu, Boying & Lin, Yingzhen, 2026. "A simplified discontinuous reproducing kernel method for impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 520(C).
    • Handle: RePEc:eee:apmaco:v:520:y:2026:i:c:s0096300326000020
    DOI: 10.1016/j.amc.2026.129950
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    References listed on IDEAS

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    1. Chen, Shu-Bo & Soradi-Zeid, Samaneh & Dutta, Hemen & Mesrizadeh, Mehdi & Jahanshahi, Hadi & Chu, Yu-Ming, 2021. "Reproducing kernel Hilbert space method for nonlinear second order singularly perturbed boundary value problems with time-delay," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    2. D. D. Bainov & S. I. Kostadinov & N. Van Minh & N. Hong Thai & P. P. Zabreiko, 1992. "Integral manifolds of impulsive differential equations," International Journal of Stochastic Analysis, Hindawi, vol. 5, pages 1-11, January.
    3. Zhang, Gui-Lai, 2022. "Convergence, consistency and zero stability of impulsive one-step numerical methods," Applied Mathematics and Computation, Elsevier, vol. 423(C).
    4. Zhang, G.L. & Song, M.H., 2015. "Asymptotical stability of Runge–Kutta methods for advanced linear impulsive differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 831-837.
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