Optimal order multistep methods with an arbitrary number of nonsteppoints

  • Tom Lyche
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 109)


In this paper optimal order, k-step methods with one nonstep point for the numerical solution of y' = f(x,y) y(a) = n, introduced by Gragg and Stetter (1) are extended to an arbitrary number s of nonstep points. These methods have order 2k + 2s, are proved stable for k ≤ 8, s ≥ 2, and not stable for large k.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Gragg, W.B., and Stetter, H.J., Generalized multistep predictor-corrector methods, J.ACM 11(1964), 188–209.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Danchick, R., Further results on generalized predictor-corrector methods. J.COMP.A.SYST.SCIEN. 2(1968), 203–218.MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Marden, M., Geometry of polynomials. American mathematical society, Providence, Rhode Island, 1966.Google Scholar

Copyright information

© Springer-Verlag 1969

Authors and Affiliations

  • Tom Lyche

There are no affiliations available

Personalised recommendations