Dontchev, A. L.; Hager, William W.; Veliov, Vladimir M. Second-order Runge-Kutta approximations in control constrained optimal control. (English) Zbl 0968.49022 SIAM J. Numer. Anal. 38, No. 1, 202-226 (2000). Summary: 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. Cited in 73 Documents MSC: 49M25 Discrete approximations in optimal control 65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations Keywords:optimal control; numerical solution; discretization; Runge-Kutta scheme; rate of convergence PDFBibTeX XMLCite \textit{A. L. Dontchev} et al., SIAM J. Numer. Anal. 38, No. 1, 202--226 (2000; Zbl 0968.49022) Full Text: DOI