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Computer Aided Analysis and Optimization of Mechanical System Dynamics pp 335–349Cite as

The Numerical Solution of Problems Which May Have High Frequency Components

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Part of the book series: NATO ASI Series ((NATO ASI F,volume 9))

Abstract

This talk surveys the state of the art of methods for solving problems which have the potential for high frequency oscillations. In some cases the oscillatory components can be damped, but in other cases they must be followed. In the latter situation it is sometimes possible to separate the system into fast and slow components. If not, direct methods for nearly periodic solutions can be used.

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References

  1. Andrus, J. F., Numerical solution of systems of ordinary differential equations separated into subsystems, SIAM J. Numerical Analysis 16 (4), August 1979, 605–611.

    Article  MathSciNet  MATH  Google Scholar 

  2. Gaffney, P. W., A survey of FORTRAN subroutines for solving stiff oscillatory ordinary differential equations, ORNL/CSD/TM-134, Oak Ridge National Laboratory, 1981.

    Google Scholar 

  3. Gallivan, K. A., An algorithm for the detection and integration of highly oscillatory ordinary differential equations using a generalized unified modified divided difference representation, Dept. Rept. R-83–1121; also, Ph.D. thesis, May 1983.

    Google Scholar 

  4. Gear, C. W., Tu, K-W., The Effect of Variable Mesh Size on the Stability of Multistep Methods, SIAM J. Numerical Analysis 11, (4), October 1974, 1025–1043.

    Article  MathSciNet  MATH  Google Scholar 

  5. Gear, C. W., Runge-Kutta starters for multistep methods, TOMS 6 (3), September 1980, 263–279.

    Article  MathSciNet  MATH  Google Scholar 

  6. Gear, C. W., Automatic treatment of stiff and/or oscillatory equations, Dept. Rept. R80–1019; Proc. Bielefeld Conference on Numerical Methods in Computational Chemistry,Bielefeld, W. Germany, 1980, in Lecture Notes in Mathematics 968,1982, 190–206.

    Google Scholar 

  7. Gear, C. W., Stiff software: what do we have and what do we need?, Proc. Intl. Con! Stiff Computation, Salt Lake City, Utah, April 12–14, 1982.

    Google Scholar 

  8. Graff, O. F. and D. G. Bettis, Modified multirevolution integration methods for satellite orbit computation, Celestial Mechanics 11, 1975, 443–448.

    Google Scholar 

  9. Graff, O. F., Methods of orbit computation with multirevolution steps, Applied Mechanics Research Laboratory Report 1063, University of Texas at Austin, 1973.

    Google Scholar 

  10. Orailoglu, A., A Multirate Ordinary Differential Equation Integrator, Dept. Rept. R-79959, March 1979.

    Google Scholar 

  11. Mace, D. and L. H. Thomas, An extrapolation method for stepping the calculations of the orbit of an artificial satellite several revolutions ahead at a time, Astronomical J. 65 (5), June 1960.

    Google Scholar 

  12. Palusinski, O. A., Simulation of dynamic systems using multirate techniques, CSRL Memo #333, Engineering Experiment Station, University of Arizona, Tuscon, Nov. 1979.

    Google Scholar 

  13. Palusinski, O. A. and J. V. Wait, Simulation methods for combined linear and nonlinear systems, Simulation 30 (3), March 1978, 85–94.

    Article  MATH  Google Scholar 

  14. Petzold, L. R., An efficient numerical method for highly oscillatory ordinary differential equations, Dept. Rept. R-78–933; also, Ph.D. Thesis 1978.

    Google Scholar 

  15. Shampine, L. F. and C. W. Gear, A user’s view of solving stiff ordinary differential equations, SIAM Review 21 (1), January 1979, 1–17.

    Article  MathSciNet  MATH  Google Scholar 

  16. Skelboe, S., Computation of the periodic steady state response of nonlinear networks by extrapolation methods, IEEE Trans. Circuits and Systems CAS-27, (3), 1980, 161–175.

    Article  MathSciNet  MATH  Google Scholar 

  17. Wells, D. R., Multirate linear multistep methods for the solution of systems of ordinary differential equations, Dept. Rept. R-82–1093; also, Ph.D. Thesis, July 1982.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Illinois at Urbana-Champaign, USA

    C. W. Gear

Authors
  1. C. W. Gear
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Editor information

Editors and Affiliations

  1. Center for Computer Aided Design, College of Engineering, University of Iowa, 52242, Iowa City, IA, USA

    Edward J. Haug

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© 1984 Springer-Verlag Berlin Heidelberg

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Gear, C.W. (1984). The Numerical Solution of Problems Which May Have High Frequency Components. In: Haug, E.J. (eds) Computer Aided Analysis and Optimization of Mechanical System Dynamics. NATO ASI Series, vol 9. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52465-3_13

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  • DOI: https://doi.org/10.1007/978-3-642-52465-3_13

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-52467-7

  • Online ISBN: 978-3-642-52465-3

  • eBook Packages: Springer Book Archive

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