Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control

We are concerned with the discretization of optimal control problems when a Runge–Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian’s first order conditions on the discrete model, require a symplectic partitioned Runge–Kutta scheme for state–costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian. We prove that a correct numerical treatment of the state–current costate system needs Lawson exponential schemes for the costate approximation. In the numerical tests a shooting strategy is employed in order to verify the accuracy, up to the fourth order, of the innovative procedure we propose.

We are concerned with the discretization of optimal control problems when a Runge Kutta scheme is selected for the related Hamiltonian system. It is known that Lagrangian's first order conditions on the discrete model, require a symplectic partitioned Runge Kutta scheme for state costate equations. In the present paper this result is extended to growth models, widely used in Economics studies, where the system is described by a current Hamiltonian. We prove that a correct numerical treatment of the state current costate system needs Lawson exponential schemes for the costate approximation. In the numerical tests a shooting strategy is employed in order to verify the accuracy, up to the fourth order, of the innovative procedure we propose. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.