Efficient Implementation of Weighted ENO Schemes

@article{Jiang1996EfficientIO,
  title={Efficient Implementation of Weighted ENO Schemes},
  author={Guang-Shan Jiang and Chi-Wang Shu},
  journal={Journal of Computational Physics},
  year={1996},
  volume={126},
  pages={202-228}
}
In this paper, we further analyze, test, modify, and improve the high order WENO (weighted essentially non-oscillatory) finite difference schemes of Liu, Osher, and Chan. It was shown by Liuet al.that WENO schemes constructed from therth order (inL1norm) ENO schemes are (r+ 1)th order accurate. We propose a new way of measuring the smoothness of a numerical solution, emulating the idea of minimizing the total variation of the approximation, which results in a fifth-order WENO scheme for the… 
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High-Order ENO and WENO Schemes with Flux Gradient and Source Term Balancing
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References

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EFFICIENT IMPLEMENTATION OF WEIGHTED ENO SCHEMES
TLDR
A new way of measuring the smoothness of a numerical solution is proposed, emulating the idea of minimizing the total variation of the approximation, which results in a 5th order WENO scheme for the case r=3, instead of the 4th order with the original smoothness measurement by Liu et al.
A numerical study of the convergence properties of ENO schemes
We report numerical results obtained with finite difference ENO schemes for the model problem of the linear convection equation with periodic boundary conditions. For the test function sin(x), the
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