Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control

F. Diele, C. Marangi and S. Ragni

Mathematics and Computers in Simulation (MATCOM), 2011, vol. 81, issue 5, 1057-1067

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.

Keywords: Partitioned Runge–Kutta methods; Exponential Lawson schemes; Optimal growth models (search for similar items in EconPapers)
Date: 2011
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:81:y:2011:i:5:p:1057-1067

DOI: 10.1016/j.matcom.2010.10.010

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