TITLE:
An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives
AUTHORS:
Jin Yao, Karl E. Nelson
KEYWORDS:
Monotone Interpolation, Quartic, Non-Oscillation Derivative, Interface Reconstruction, Slope Space, Hermit Spline
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.8 No.1,
January
24,
2018
ABSTRACT: A
one-dimensional monotone interpolation method based on interface reconstruction
with partial volumes in the slope-space utilizing the Hermite cubic-spline, is
proposed. The new method is only quartic, however is C2 and unconditionally monotone. A set of control points is employed to
constrain the curvature of the interpolation function and to eliminate possible
nonphysical oscillations in the slope space. An extension of this method in
two-dimensions is also discussed.