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The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note

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  • Juan Zhang
  • Mei Sun
  • Enran Hou
  • Zhaoxing Ma
  • Efthymios G. Tsionas

Abstract

The traditional radial basis function parameter controls the flatness of these functions and influences the precision and stability of approximation solution. The coupled radial basis function, which is based on the infinitely smooth radial basis functions and the conical spline, achieves an accurate and stable numerical solution, while the shape parameter values are almost independent. In this paper, we give a quasi-optimal conical spline which can improve the numerical results. Besides, we consider the collocation points in the Chebyshev-type which improves solution accuracy of the method with no additional computational cost.

Suggested Citation

  • Juan Zhang & Mei Sun & Enran Hou & Zhaoxing Ma & Efthymios G. Tsionas, 2021. "The Quasi-Optimal Radial Basis Function Collocation Method: A Technical Note," Journal of Mathematics, Hindawi, vol. 2021, pages 1-5, September.
    • Handle: RePEc:hin:jjmath:6694369
    DOI: 10.1155/2021/6694369
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