Improved Bettis Methods for Long-Term Prediction

  • José M. Ferrándiz
  • Sylvia Novo
Part of the NATO ASI Series book series (NSSB, volume 272)


In this paper we introduce a modification of Bettis’ method in order to improve the long-term numerical integration of perturbed oscillators. We give several examples, involving both single and coupled oscillators, to illustrate the efficiency of this approach with respect to the methods of Bettis and Adams-Bashforth.


Cauchy Problem Perturbation Technique Couple Oscillator Error Growth Symplectic Integrator 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Bettis, D.G., 1970, Numerical Integration of Products of Fourier and Ordinary Polynomials. Numer,Math., 14, 421:434.MathSciNetGoogle Scholar
  2. [2]
    Bettis, D.G., 1970, Stabilization of Finite Difference Methods of Numerical Integration. Celest.Mech.,, 2, 282:295.MathSciNetGoogle Scholar
  3. Ferrándiz, J.M. and Pérez M.T.,1990, Application of Spherically Exact Algorithms to Numerical Predictability in Two-Body Problems. In this issue.Google Scholar
  4. [4]
    Kinoshita H., Yoshida H. and Nakai H., 1990, Symplectic Integrators and Their Merits in Application to Dynamical Astronomy, in: Proceedings of the twentythird Symposium on ℌCelestial Mechanicsℍ, Kinoshita, H. and Yoshida, H. eds., Kyoto, Japan.Google Scholar
  5. [5]
    Kinoshita H. and Nakai H., 1989, Numerical Integration Methods in Dynamical Astronomy.Celest.Mech.,, 45, 231:244.Google Scholar
  6. [6]
    Kirchgraber U., 1989, An ODE-Solver Based on the Method of Averaging. Numer.Math.,, 53, 621:652.MathSciNetGoogle Scholar
  7. [7]
    Stiefel, E. and Scheifele, G., 1971, ℌLinear and Regular Celestial Mechanicsℍ. Springer. Berlin, Heidelberg, New York.MATHGoogle Scholar

Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • José M. Ferrándiz
    • 1
  • Sylvia Novo
    • 1
  1. 1.Departamento de Matemática Aplicada a la Ingeniería E.T.S. de Ingenieros IndustrialesUniversidad de ValladolidValladolidSpain

Personalised recommendations