DIAGONALLY IMPLICIT GENERAL LINEAR METHODS FOR ORDINARY DIFFERENTIAL-EQUATIONS

We investigate some classes of general linear methods with s internal and r external approximations, with stage order q and order p, adjacent to the class with s = r = q = p considered by Butcher. We demonstrate that interesting methods exist also if s + 1 = r = q, p = q or q + 1, s = r + 1 = q, p = q or q + 1, and s = r = q, p = q + 1. Examples of such methods are constructed with stability function matching the A-acceptable generalized Pade approximations to the exponential function.