Further results on generalized predictor-corrector methods

  • Authors:
  • Roy Danchick

  • Affiliations:
  • -

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 1968

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Abstract

In this paper we extend from k=4 to k=6 the existence of a stable maximal order (2k+2), generalized multistep predictor-corrector methods for the solution of the initial-value problem y^'(x)=f(x,y),y(0)=y"0. The existence of such method for k=1, 2, 3, and 4 was first demonstrated by Gragg and Stetter. The key notion utilized in our derivations is, similar to that described by Butcher, a quasi-Hermite Interpolating Polynomial, H, over the points 0, 1, 2, ..., k-1, @q where k-1