Author(s)

Jin Yao, Karl E. Nelson

Lawrence Livermore National Laboratory, Livermore, CA, USA.

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.

Monotone Interpolation, Quartic, Non-Oscillation Derivative, Interface Reconstruction, Slope Space, Hermit Spline

Yao, J. and Nelson, K. (2018) An Unconditionally Monotone C² Quartic Spline Method with Nonoscillation Derivatives. Advances in Pure Mathematics, 8, 25-40. doi: 10.4236/apm.2018.81003.