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.