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Order conditions for a class of two-step methods for y '' =f(x,y). (English) Zbl 1022.65080
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.

MSC:
65L06Multistep, Runge-Kutta, and extrapolation methods
34A34Nonlinear ODE and systems, general
65L05Initial value problems for ODE (numerical methods)
65L20Stability and convergence of numerical methods for ODE