Further results on generalized predictor-corrector methods

✍ Scribed by Roy Danchick

• Publisher: Elsevier Science
• Year: 1968
• Tongue: English
• Weight: 479 KB
• Volume: 2
• Category: Article
• ISSN: 0022-0000
• DOI: 10.1016/s0022-0000(68)80032-7

✦ Synopsis

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

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, O where k --1 < 0 < k. From this notion follows a new characterization of the order-maximizing off-grid point 8. This characterization, in turn, leads us to the development of an explicit corrector truncation error formula.