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A high order essentially non-oscillatory shock capturing method. (English) Zbl 0617.65095
Large scale scientific computing, Proc. Meet., Oberwolfach/FRG 1985, Prog. Sci. Comput. 7, 197-208 (1987).
[For the entire collection see Zbl 0614.00022.]
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.
MSC:
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws