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Meshfree approach for solving multi-dimensional systems of Fredholm integral equations via barycentric Lagrange interpolation

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  • Liu, Hongyan
  • Huang, Jin
  • Zhang, Wei
  • Ma, Yanying

Abstract

A highly accurate meshfree approach based on the barycentric Lagrange basis functions is reported for solving the linear and nonlinear multi-dimensional systems of Fredholm integral equations (FIEs) of the second kind. The method is an improved Lagrange interpolation technique which possesses high precision and inexpensive procedure. The systems of FIEs are handled with the barycentric formula and transformed into the corresponding linear and nonlinear systems of algebraic equations. The stability of the solved integral equation systems is guaranteed by the numerical stability of the barycentric Lagrange formula, which is dominated by barycentric weights. The convergence analysis and error estimation are included. Some computational results indicate that the method is simple and efficient.

Suggested Citation

  • Liu, Hongyan & Huang, Jin & Zhang, Wei & Ma, Yanying, 2019. "Meshfree approach for solving multi-dimensional systems of Fredholm integral equations via barycentric Lagrange interpolation," Applied Mathematics and Computation, Elsevier, vol. 346(C), pages 295-304.
    • Handle: RePEc:eee:apmaco:v:346:y:2019:i:c:p:295-304
    DOI: 10.1016/j.amc.2018.10.024
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    Cited by:

    1. Liu, Hongyan & Huang, Jin & Zhang, Wei, 2021. "Numerical algorithm based on extended barycentric Lagrange interpolant for two dimensional integro-differential equations," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Torkaman, Soraya & Heydari, Mohammad & Loghmani, Ghasem Barid, 2023. "A combination of the quasilinearization method and linear barycentric rational interpolation to solve nonlinear multi-dimensional Volterra integral equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 366-397.

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