Coleman, John P. Order conditions for a class of two-step methods for \(y''=f(x,y)\). (English) Zbl 1022.65080 IMA J. Numer. Anal. 23, No. 2, 197-220 (2003). The determination of the order of a two-step hybrid method is reduced to checking that certain relationships between the coefficients are satisfied. This approach which use the theory of B-series is an alternative to the usually method to derive order conditions by ad hoc expansions in Taylor series which are specific to the particular method. The results of the paper are applicable to almost all hybrid methods. Furthermore, conditions under which the two-step methods are symmetric are established and particular examples are considered. Reviewer: Dana Petcu (Timişoara) Cited in 2 ReviewsCited in 68 Documents MSC: 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations 34A34 Nonlinear ordinary differential equations and systems 65L05 Numerical methods for initial value problems involving ordinary differential equations 65L20 Stability and convergence of numerical methods for ordinary differential equations Keywords:order conditions; two-step methods; B-series; numerical examples PDFBibTeX XMLCite \textit{J. P. Coleman}, IMA J. Numer. Anal. 23, No. 2, 197--220 (2003; Zbl 1022.65080) Full Text: DOI