High Order Strong Stability Preserving Time Discretizations
Journal of Scientific Computing
Numerical invariantization for morphological PDE schemes
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
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SIAM Journal on Numerical Analysis
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In this note we show that when a discontinuous initial value problem for a scalar hyperbolic equation in one space variable is approximated by a difference scheme that is more than first order accurate; it leads to overshoots analogous to the Gibbs phenomenon when discontinuous functions are approximated by sections of Fourier series. A hybrid scheme due to Harten and Zwass removes the overshoots. Similar phenomena occur when solving schemes of hyperbolic equations.