An Unconditionally Monotone C^{2} Quartic Spline Method with Nonoscillation Derivatives
Abstract
Here, a onedimensional monotone interpolation method based on interface reconstruction with partial volumes in the slopespace utilizing the Hermite cubicspline, is proposed. The new method is only quartic, however is C^{2} 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 twodimensions is also discussed.
 Authors:

 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1420288
 Report Number(s):
 LLNLJRNL742107
Journal ID: ISSN 21600368
 Grant/Contract Number:
 AC5207NA27344
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Advances in Pure Mathematics
 Additional Journal Information:
 Journal Volume: 8; Journal Issue: 1; Journal ID: ISSN 21600368
 Publisher:
 Scientific Research Publishing, Inc.
 Country of Publication:
 United States
 Language:
 English
 Subject:
 97 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; Monotone Interpolation; Quartic; NonOscillation Derivative; Interface Reconstruction; Slope Space; Hermit Spline
Citation Formats
Yao, Jin, and Nelson, Karl E. An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives. United States: N. p., 2018.
Web. doi:10.4236/apm.2018.81003.
Yao, Jin, & Nelson, Karl E. An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives. United States. doi:10.4236/apm.2018.81003.
Yao, Jin, and Nelson, Karl E. Wed .
"An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives". United States. doi:10.4236/apm.2018.81003. https://www.osti.gov/servlets/purl/1420288.
@article{osti_1420288,
title = {An Unconditionally Monotone C2 Quartic Spline Method with Nonoscillation Derivatives},
author = {Yao, Jin and Nelson, Karl E.},
abstractNote = {Here, a onedimensional monotone interpolation method based on interface reconstruction with partial volumes in the slopespace utilizing the Hermite cubicspline, 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 twodimensions is also discussed.},
doi = {10.4236/apm.2018.81003},
journal = {Advances in Pure Mathematics},
number = 1,
volume = 8,
place = {United States},
year = {2018},
month = {1}
}
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