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The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel

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  • Alvandi, Azizallah
  • Paripour, Mahmoud

Abstract

The reproducing kernel method is applied to Volterra nonlinear integro-differential equations. In this technique, the nonlinear term is replaced by its Taylor series. The exact solution is represented in the form of series in the reproducing Hilbert kernel space. The approximation solution is expressed by n-term summation of reproducing kernel functions. Some numerical examples are solved in two different spaces and parameters of n. Measurements of the experimental data is an indications of stability and convergence on the reproducing kernel.

Suggested Citation

  • Alvandi, Azizallah & Paripour, Mahmoud, 2019. "The combined reproducing kernel method and Taylor series for handling nonlinear Volterra integro-differential equations with derivative type kernel," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 151-160.
    • Handle: RePEc:eee:apmaco:v:355:y:2019:i:c:p:151-160
    DOI: 10.1016/j.amc.2019.02.023
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    References listed on IDEAS

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    1. Omar Abu Arqub & Mohammed Al-Smadi & Shaher Momani, 2012. "Application of Reproducing Kernel Method for Solving Nonlinear Fredholm-Volterra Integrodifferential Equations," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-16, September.
    2. Biazar, J. & Ghazvini, H. & Eslami, M., 2009. "He’s homotopy perturbation method for systems of integro-differential equations," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1253-1258.
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    Cited by:

    1. Musa Cakir & Baransel Gunes, 2022. "A Fitted Operator Finite Difference Approximation for Singularly Perturbed Volterra–Fredholm Integro-Differential Equations," Mathematics, MDPI, vol. 10(19), pages 1-19, September.
    2. 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).
    3. 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).

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