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Numerische Mathematik

, Volume 19, Issue 1, pp 65–75 | Cite as

Chebyshevian multistep methods for ordinary differential equations

  • Tom Lyche
Article

Summary

In this paper some theory of linear multistep methods fory(r)(x)=f(x,y) is extended to include smooth, stepsize-dependent coefficients. Treated in particular is the case where exact integration of a given set of functions is desired.

Keywords

Differential Equation Ordinary Differential Equation Mathematical Method Multistep Method Linear Multistep Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    Dahlquist, G.: Convergence and stability in the numerical integration of ordinary differential equations. Math. Scand.4, 33–53 (1956).Google Scholar
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    Gautschi, W.: Numerical integration of ordinary differential equations based on trigonometric polynomials. Numer. Math.3, 381–397, (1961).Google Scholar
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    Henrici, P.: Discrete variable methods in ordinary differential equations. New York: Wiley 1962.Google Scholar
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    Salzer, H. E.: Trigonometric interpolation and predictor-corrector formulas for numerical integration. ZAMM42, 403–412 (1962).Google Scholar
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    Stiefel, E., Bettis, D. G.: Stabilization of Cowells method Numer. Math.13, 154–175 (1969).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Tom Lyche
    • 1
    • 2
  1. 1.Center for Numerical Analysis the University of Texas at AustinUSA
  2. 2.Department of MathematicsUniversity of OsloOslo 3Norway

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