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The radial basis function differential quadrature method with ghost points

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  • Lin, Ji
  • Zhao, Yuxiang
  • Watson, Daniel
  • Chen, C.S.

Abstract

We propose a simple approach to improve the accuracy of the Radial Basis Function Differential Quadrature (RBF-DQ) method for the solution of elliptic boundary value problems. While the traditional RBF-DQ method places the centers exclusively inside the domain, the proposed method expands the region for the centers allowing them to lie both inside and outside the computational domain. Furthermore, we seek an improvement to determine the shape parameter for the radial basis function by using the modified Franke’s formula to find an initial search interval for the leave-one-out cross-validation method, which is a widely used method for the determination of the shape parameter. Both 2D and 3D numerical examples are presented to demonstrate the effectiveness of the proposed method.

Suggested Citation

  • Lin, Ji & Zhao, Yuxiang & Watson, Daniel & Chen, C.S., 2020. "The radial basis function differential quadrature method with ghost points," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 173(C), pages 105-114.
    • Handle: RePEc:eee:matcom:v:173:y:2020:i:c:p:105-114
    DOI: 10.1016/j.matcom.2020.01.006
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    References listed on IDEAS

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    1. Wu, Hui-Yuan & Duan, Yong, 2016. "Multi-quadric quasi-interpolation method coupled with FDM for the Degasperis–Procesi equation," Applied Mathematics and Computation, Elsevier, vol. 274(C), pages 83-92.
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    Cited by:

    1. Zhu, Xiaomin & Dou, Fangfang & Karageorghis, Andreas & Chen, C.S., 2020. "A fictitious points one–step MPS–MFS technique," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    2. Ma, Y. & Chen, C.S. & Hon, Y.C., 2025. "A novel meshless method for solving long-term evolution problem on irregular domain," Applied Mathematics and Computation, Elsevier, vol. 490(C).
    3. Ku, Cheng-Yu & Xiao, Jing-En & Liu, Chih-Yu & Lin, Der-Guey, 2021. "On solving elliptic boundary value problems using a meshless method with radial polynomials," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 185(C), pages 153-173.

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