Polynomial interpolation schemes for internal derivative distributions on structured grids
type: Item
instance of: scholarly article
title: Polynomial interpolation schemes for internal derivative distributions on structured grids
zbMATH Open document ID: 0826.65004
DOI: 10.1016/0168-9274(95)00014-L
author: William S. Russell
published in: Applied Numerical Mathematics
publication date: 1995-07-04T00:00:00Z
review text: The problem of finding interpolation schemes for a given function distribution on a two-dimensional grid, eventually involves interpolation over the corresponding derivative field. The author obtains a formulation of certain schemes which may produce smooth distributions, accurate results, and computational efficiency. Smoothness property is required because discontinuities in slope cannot be admitted when flow fields are modeled as nonlinear functions. In this direction bicubic, biquintic, cubic-linear and quintic-cubic schemes are considered to interpolate over both function and derivative fields. Some numerical results allow the reader to appraise a method as compared with another. Astrophysical \(N\)-body computations and particle trajectories in oceanic flows are discussed in details as two outstanding applications of these techniques.
Mathematics Subject Classification ID: 65D05
Mathematics Subject Classification ID: 65D25
Mathematics Subject Classification ID: 41A05
Mathematics Subject Classification ID: 41A63
Mathematics Subject Classification ID: 70F10
zbMATH DE Number: 770319
zbMATH Keywords: finite difference approximations
zbMATH Keywords: bicubic scheme
zbMATH Keywords: biquintic scheme
zbMATH Keywords: cubic-linear scheme
zbMATH Keywords: astrophysical \(N\)-body computations
zbMATH Keywords: interpolation schemes
zbMATH Keywords: quintic-cubic schemes
zbMATH Keywords: numerical results
zbMATH Keywords: oceanic flows
reviewed by: J. Illán
MaRDI profile type: Publication
cites work: A numerical method for the Study of the circulation of the world ocean
cites work: An Error Analysis for Numerical Differentiation
full work available at URL: 0168-9274(95)00014-l
OpenAlex ID: W1986933194
description: scientific article; zbMATH DE number 770319