A new class of non-linear monotone Hermite interpolants

作者：Arandiga Francesc^*; Baeza Antonio; Yanez Dionisio F

来源：Advances in Computational Mathematics, 2013, 39(2): 289-309.

DOI：10.1007/s10444-012-9280-1

• Interpolation
• Monotonicity
• Hermite
• Non-linear

Monotonicity-preserving approximation methods are used in numerous applications. These methods are expected to reconstruct a function from a discrete set of data preserving Monotonicity properties (i.e., the reconstructed function has to be monotone wherever the discrete data are). Most Monotonicity-preserving methods sacrifice accuracy in order to obtain Monotonicity. In this work we propose and analyze a Monotonicity-preserving Hermite interpolant that does not fully sacrifice accuracy. A key ingredient in the proposed technique is the approximation of derivatives using ENO (Essentially Non Oscillatory) and WENO (Weighted Essentially Non Oscillatory) interpolatory techniques. Then, an appropriate filtering process ensures the preservation of Monotonicity while maintaining, at the same time, the order of accuracy as high as possible. We perform several numerical experiments which confirm the properties of the proposed algorithms and compare them to other standard interpolatory approximation techniques.

• 出版日期2013-8