High Order Integration of Smooth Dynamical Systems: Theory and Numerical Experiments

Abstract

This paper describes a new class of algorithms for integrating linear second order equations and those containing smooth nonlinearities. The algorithms are based on a combination of ideas from standard Newmark integration methods and extrapolation techniques. For the algorithm to work the underlying Newmark method must be stable second order accurate, and produce asymptotic error expansions for response quantities containing only even ordered terms. It is proved that setting the Newmark parameter Gamma to 1/2 gives a desirable asymptotic expansion, irrespective of the setting for Beta. Numerical experiments are conducted for two linear and two nonlinear applications.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 1991
Accession Number
ADA445569

Entities

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  • M. E. Austin

Organizations

  • University of Maryland

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Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Regression Analysis.