Runge–Kutta methods for affinely controlled nonlinear systems

Rooted tree analysis is adapted from stochastic differential equations to derive systematically general Runge–Kutta methods for deterministic affinely controlled nonlinear systems. Order conditions are found and some specific coefficients for second- and third-order methods are determined, which are then used for simulations compared with the Taylor methods for affinely controlled nonlinear systems derived by Grüne and Kloeden.