# 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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## References

SHOWING 1-10 OF 23 REFERENCES

### EFFICIENT IMPLEMENTATION OF WEIGHTED ENO SCHEMES

- Computer Science
- 1995

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

- Mathematics
- 1990

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…

### Uniformly high order accurate essentially non-oscillatory schemes, 111

- Computer Science, Mathematics
- 1987

### 91-1557, in AIAA 10th Computational Fluid 12

- A. Rogerson and E. Meiberg, J. Sci. Comput. 5, 151 (1990). Dynamics Conference, Honolulu, Hawaii, June
- 1991

### Commun. Pure Appl. Math. J. Comput. Phys

- Commun. Pure Appl. Math. J. Comput. Phys
- 1954

### J. Comput. Phys

- J. Comput. Phys
- 1994

### Division of Applied Mathematics, Brown 18

- G. Strang, Numer. Math
- 1964

### J. Comput. Phys

- J. Comput. Phys
- 1978