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(h2 ) where h is the mesh spacing.