Implicit Runge–Kutta Schemes for Optimal Control Problems with Evolution Equations

Abstract In this paper we discuss the use of implicit Runge–Kutta schemes for time discretization optimal control problems with evolution equations. The specialty considered discretizations is that state and adjoint are chosen such optimization commute. It well known property additional order conditions necessary. We give sufficient which class these condition automatically fulfilled. focus especially on Gauss, Radau IA, IIA, Lobatto IIIA, IIIB IIIC collocation type up to six. Furthermore, also a SDIRK (singly diagonally Runge–Kutta) method demonstrate, general methods not Numerical examples illustrate predicted convergence rates.