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Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control

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  • Diele, F.
  • Marangi, C.
  • Ragni, S.

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.

Suggested Citation

  • Diele, F. & Marangi, C. & Ragni, S., 2011. "Exponential Lawson integration for nearly Hamiltonian systems arising in optimal control," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(5), pages 1057-1067.
    • Handle: RePEc:eee:matcom:v:81:y:2011:i:5:p:1057-1067
    DOI: 10.1016/j.matcom.2010.10.010
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    References listed on IDEAS

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    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, December.
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    3. Ben R. Craig & William E. Jackson & James B. Thomson, 2004. "On SBA-guaranteed lending and economic growth," Working Papers (Old Series) 0403, Federal Reserve Bank of Cleveland.
    4. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
    5. Miguel-Angel Martín & Agustín Herranz, 2004. "Human capital and economic growth in Spanish regions," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 10(4), pages 257-264, November.
    6. Ragni, Stefania & Diele, Fasma & Marangi, Carmela, 2010. "Steady-state invariance in high-order Runge-Kutta discretization of optimal growth models," Journal of Economic Dynamics and Control, Elsevier, vol. 34(7), pages 1248-1259, July.
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    Cited by:

    1. Fasma Diele & Carmela Marangi, 2019. "Geometric Numerical Integration in Ecological Modelling," Mathematics, MDPI, vol. 8(1), pages 1-30, December.
    2. Antoci, Angelo & Ragni, Stefania & Russu, Paolo, 2016. "Optimal dynamics in a two-sector model with natural resources and foreign direct investments," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 290-307.

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