Second-order Runge-Kutta approximations in control constrained optimal control

In this paper, we analyze second-order Runge-Kutta approximations to a nonlinear optimal control problem with control constraints. If the optimal control has a derivative of bounded variation and a coercivity condition holds, we show that for a special class of Runge Kutta schemes, the error in the discrete approximating control is O(h(2)) where h is the mesh spacing.