University of Illinois Urbana-Champaign

Piecewise polynomials and partition method for ordinary differential equations

Langhaar, Henry L.; Chu, S.C.

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https://hdl.handle.net/2142/112024

Description

Title
Piecewise polynomials and partition method for ordinary differential equations
Author(s)
  • Langhaar, Henry L.
  • Chu, S.C.
Issue Date
1967-09
Keyword(s)
  • Piecewise Polynomials
  • Partition Method
  • Ordinary Differential Equations
Abstract
The distinctive mathematical feature of the flexible finite-element method is the use of piecewise analytic approximations. The region under consideration is partitioned into cells somewhat arbitrarily and, in each cell, simple approximating functions are chosen—usually polynomials of a low degree. Some continuity conditions are imposed at the boundaries of the cells, but ordinarily the derivatives above the first order are not required to be continuous. Various methods, such as collocation, least squares, and orthogonality are available for liquidating residuals, but, so far, matrix formulations derivable from energy principles have been used. Implicitly, this is the Rayleigh-Ritz method. In this investigation, the piecewise polynomial approximation is applied to ordinary differential equations. A method of sub-partitioning is used to liquidate residuals. The procedure appears to be competitive with the finite-difference method.
Publisher
Department of Theoretical and Applied Mechanics. College of Engineering. University of Illinois at Urbana-Champaign
Series/Report Name or Number
  • TAM R 301
  • 1967-0715
ISSN
0073-5264
Type of Resource
text
Language
eng
Permalink
http://hdl.handle.net/2142/112024
Sponsor(s)/Grant Number(s)
National Science Foundation Grant NSF GK 604
Copyright and License Information
Copyright 1967 Board of Trustees of the University of Illinois

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Technical Reports - Theoretical and Applied Mechanics (TAM) PRIMARY
TAM technical reports include manuscripts intended for publication, theses judged to have general interest, notes prepared for short courses, symposia compiled from outstanding undergraduate projects, and reports prepared for research-sponsoring agencies.