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Accurate Monotone Cubic Interpolation

1993; Society for Industrial and Applied Mathematics; Volume: 30; Issue: 1 Linguagem: Inglês

10.1137/0730004

1095-7170

Hung T. Huynh,

Advanced Numerical Methods in Computational Mathematics

Monotone piecewise cubic interpolants are simple and effective. They are generally third-order accurate, except near strict local extrema where accuracy degenerates to second order due to the monotonicity constraint. Algorithms for piecewise cubic interpolants that preserve monotonicity as well as uniform third- and fourth-order accuracy are presented. The gain of accuracy is obtained by relaxing the monotonicity constraint in a geometric framework in which the median function plays a crucial role. These algorithms can also be applied to the reconstruction step in shock-capturing methods for conservation laws.