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Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions

Author

Listed:
  • Pedro González-Rodelas

    (Department of Applied Mathematics, Granada University, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Miguel Pasadas

    (Department of Applied Mathematics, Granada University, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Abdelouahed Kouibia

    (Department of Applied Mathematics, Granada University, 18071 Granada, Spain
    These authors contributed equally to this work.)

  • Basim Mustafa

    (Department of Applied Mathematics, Granada University, 18071 Granada, Spain
    These authors contributed equally to this work.)

Abstract

In this paper we propose an approximation method for solving second kind Volterra integral equation systems by radial basis functions. It is based on the minimization of a suitable functional in a discrete space generated by compactly supported radial basis functions of Wendland type. We prove two convergence results, and we highlight this because most recent published papers in the literature do not include any. We present some numerical examples in order to show and justify the validity of the proposed method. Our proposed technique gives an acceptable accuracy with small use of the data, resulting also in a low computational cost.

Suggested Citation

  • Pedro González-Rodelas & Miguel Pasadas & Abdelouahed Kouibia & Basim Mustafa, 2022. "Numerical Solution of Linear Volterra Integral Equation Systems of Second Kind by Radial Basis Functions," Mathematics, MDPI, vol. 10(2), pages 1-15, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:223-:d:722768
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    Citations

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    Cited by:

    1. Abdelouahed Kouibia & Pedro González & Miguel Pasadas & Bassim Mustafa & Hossain Oulad Yakhlef & Loubna Omri, 2024. "Approximation of Bivariate Functions by Generalized Wendland Radial Basis Functions," Mathematics, MDPI, vol. 12(16), pages 1-10, August.
    2. Yanming Xu & Haozhi Li & Leilei Chen & Juan Zhao & Xin Zhang, 2022. "Monte Carlo Based Isogeometric Stochastic Finite Element Method for Uncertainty Quantization in Vibration Analysis of Piezoelectric Materials," Mathematics, MDPI, vol. 10(11), pages 1-17, May.

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