| Uniformly high order accurate finite difference schemes for the weak solutions of hyperbolic conservation laws are constructed. The schemes are of Strictly Non-Oscillatory in the sense that, for scalar problems, the number of local extrema of the discrete solution is not increasing in time. The design of the schemes is based on a new piecewise polynomial interpolation technique which is monotonicity preserving. Preliminary numerical results are very encouraging for model problems and for two-dimensional gas dynamics. |
