The error behaviour of a general class of predictor-corrector methods (Q1181524)

For solving nonstiff differential equations block methods offer the advantage on parallel computers that individual processors can compute independently the approximating values at different grid points. For investigating the discretization error, the order conditions, and the stability of an \(\ell\)- block predictor-corrector method it is reformulated as a block multivalue method. In the paper it is shown that this concept facilitates the analysis of the order, the stability and error behaviour of a great class of methods that are well suited for an efficient implementation in a parallel environment. The theory of Butcher series is applied successfully together with the usual concept of trees allowing the examination of two classes of methods, for which the main properties are derived.