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Application of Radial Basis Function Method for Solving Nonlinear Integral Equations

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Listed:
  • Huaiqing Zhang
  • Yu Chen
  • Chunxian Guo
  • Zhihong Fu

Abstract

The radial basis function (RBF) method, especially the multiquadric (MQ) function, was proposed for one‐ and two‐dimensional nonlinear integral equations. The unknown function was firstly interpolated by MQ functions and then by forming the nonlinear algebraic equations by the collocation method. Finally, the coefficients of RBFs were determined by Newton’s iteration method and an approximate solution was obtained. In implementation, the Gauss quadrature formula was employed in one‐dimensional and two‐dimensional regular domain problems, while the quadrature background mesh technique originated in mesh‐free methods was introduced for irregular situation. Due to the superior interpolation performance of MQ function, the method can acquire higher accuracy with fewer nodes, so it takes obvious advantage over the Gaussian RBF method which can be revealed from the numerical results.

Suggested Citation

  • Huaiqing Zhang & Yu Chen & Chunxian Guo & Zhihong Fu, 2014. "Application of Radial Basis Function Method for Solving Nonlinear Integral Equations," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:381908
    DOI: 10.1155/2014/381908
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    References listed on IDEAS

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    1. Huaiqing Zhang & Yu Chen & Xin Nie, 2014. "Solving the Linear Integral Equations Based on Radial Basis Function Interpolation," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    2. Huaiqing Zhang & Yu Chen & Xin Nie, 2014. "Solving the Linear Integral Equations Based on Radial Basis Function Interpolation," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-8, June.
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