Abstract
A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define the smoothness parameter in the non-linear weights of new WENO schemes. The main significant features of these new ENO and WENO schemes are that they are less oscillatory and achieve their relevant order of accuracy in the presence of critical points in the exact solution. It is shown theoretically as well as computationally in L1 and L∞ norm. Moreover, computational results are given to show less oscillatory behaviour of the new WENO scheme compared to WENO5-JS and WENO5-Z schemes.
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