A High Order Essentially Non-Oscillatory Shock Capturing Method
A special class of shock capturing methods for the approximation of hyperbolic conservation laws is presented. This class of methods produce essentially non-oscillatory solutions. This means that a Gibbs phenomenon at discontinuities is avoided and the variation of the numerical approximation may only grow due to the truncation error in the smooth part of the solution. The schemes have thus many of the desirable properties of total variation diminishing schemes, but they have the advantage that any order of accuracy can be achieved.
KeywordsDivided Difference Primitive Function Gibbs Phenomenon Piecewise Smooth Function Piecewise Polynomial Function
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