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Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments

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  • Li, Xiuying
  • Li, Haixia
  • Wu, Boying

Abstract

In this paper, we introduce a piecewise reproducing kernel method for impulsive delay differential equations with piecewise constant arguments. The method is an improved reproducing kernel method. Compared with the classical reproducing kernel method, the solutions obtained using the present method can give good approximations for a larger time interval. Some numerical examples are used to show the effectiveness and simplicity of the method.

Suggested Citation

  • Li, Xiuying & Li, Haixia & Wu, Boying, 2019. "Piecewise reproducing kernel method for linear impulsive delay differential equations with piecewise constant arguments," Applied Mathematics and Computation, Elsevier, vol. 349(C), pages 304-313.
    • Handle: RePEc:eee:apmaco:v:349:y:2019:i:c:p:304-313
    DOI: 10.1016/j.amc.2018.12.054
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    References listed on IDEAS

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    1. Liu, X. & Zeng, Y.M., 2018. "Linear multistep methods for impulsive delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 555-563.
    2. Ghasemi, M. & Fardi, M. & Khoshsiar Ghaziani, R., 2015. "Numerical solution of nonlinear delay differential equations of fractional order in reproducing kernel Hilbert space," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 815-831.
    3. X. Liu & M. H. Song & M. Z. Liu, 2012. "Linear Multistep Methods for Impulsive Differential Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2012, pages 1-14, May.
    4. Zhang, G.L. & Song, Minghui & Liu, M.Z., 2015. "Asymptotical stability of the exact solutions and the numerical solutions for a class of impulsive differential equations," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 12-21.
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    Cited by:

    1. Xiao Zhang & Feng Ding & Ling Xu & Ahmed Alsaedi & Tasawar Hayat, 2019. "A Hierarchical Approach for Joint Parameter and State Estimation of a Bilinear System with Autoregressive Noise," Mathematics, MDPI, vol. 7(4), pages 1-17, April.
    2. Hao Ma & Jian Pan & Lei Lv & Guanghui Xu & Feng Ding & Ahmed Alsaedi & Tasawar Hayat, 2019. "Recursive Algorithms for Multivariable Output-Error-Like ARMA Systems," Mathematics, MDPI, vol. 7(6), pages 1-18, June.
    3. Geng, F.Z. & Wu, X.Y., 2021. "Reproducing kernel function-based Filon and Levin methods for solving highly oscillatory integral," Applied Mathematics and Computation, Elsevier, vol. 397(C).
    4. Hartung, Ferenc, 2022. "On numerical approximation of a delay differential equation with impulsive self-support condition," Applied Mathematics and Computation, Elsevier, vol. 418(C).
    5. Li, X.Y. & Wu, B.Y., 2020. "A new kernel functions based approach for solving 1-D interface problems," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    6. Lijuan Wan & Ximei Liu & Feng Ding & Chunping Chen, 2019. "Decomposition Least-Squares-Based Iterative Identification Algorithms for Multivariable Equation-Error Autoregressive Moving Average Systems," Mathematics, MDPI, vol. 7(7), pages 1-20, July.
    7. Feng Ding & Jian Pan & Ahmed Alsaedi & Tasawar Hayat, 2019. "Gradient-Based Iterative Parameter Estimation Algorithms for Dynamical Systems from Observation Data," Mathematics, MDPI, vol. 7(5), pages 1-15, May.
    8. Allahviranloo, Tofigh & Sahihi, Hussein, 2021. "Reproducing kernel method to solve fractional delay differential equations," Applied Mathematics and Computation, Elsevier, vol. 400(C).

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