Abstract
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.
Anno
2011
Autori IAC
Tipo pubblicazione
Altri Autori
Diele Fasma; Marangi Carmela; Ragni Stefania
Editore
North-Holland Publishing Company
Rivista
Mathematics and computers in simulation (Print)