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Order conditions for numerical methods for partitioned ordinary differential equations

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Published in Numerische Mathematik. 1981, vol. 36, no. 4, p. 431-445
Abstract 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 for y'=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 of P-series will be used for the derivation of order conditions for Runge-Kutta-type methods for Volterra integral equations [1].
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HAIRER, Ernst. Order conditions for numerical methods for partitioned ordinary differential equations. In: Numerische Mathematik, 1981, vol. 36, n° 4, p. 431-445. https://archive-ouverte.unige.ch/unige:12454

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