Further results on generalized predictor-corrector methods

摘要

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)=y0.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, θ where k−1<θ