Radial Basis Function ENO and WENO Finite Difference Methods Based on the Optimization of Shape Parameters

@article{Guo2017RadialBF,
  title={Radial Basis Function ENO and WENO Finite Difference Methods Based on the Optimization of Shape Parameters},
  author={Jingyang Guo and Jae-Hun Jung},
  journal={Journal of Scientific Computing},
  year={2017},
  volume={70},
  pages={551-575}
}
  • J. Guo, Jae-Hun Jung
  • Published 31 January 2016
  • Mathematics, Computer Science
  • Journal of Scientific Computing
We present adaptive finite difference ENO/WENO methods with infinitely smooth radial basis functions (RBFs). These methods slightly perturb the polynomial reconstruction coefficients with RBFs as the reconstruction basis and enhance accuracy in the smooth region by locally optimizing the shape parameters. Compared to the classical ENO/WENO methods, the RBF-ENO/WENO methods provide more accurate reconstructions and sharper solution profiles near the jump discontinuity. Furthermore the RBF-ENO… 
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