, Volume 36, Issue 4, pp 431-445

Order conditions for numerical methods for partitioned ordinary differential equations

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Motivated by the consideration of Runge-Kutta formulas for partitioned systems, the theory of “P-series” is studied. This theory yields the general structure of the order conditions for numerical methods for partitioned systems, and in addition for Nyström methods fory″=f(y,y′), for Rosenbrock-type methods with inexact Jacobian (W-methods). It is a direct generalization of the theory of Butcher series [7, 8]. In a later publication, the theory ofP-series will be used for the derivation of order conditions for Runge-Kutta-type methods for Volterra integral equations [1].