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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. 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.
    2. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, September.
    3. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711, April.
    4. Mercenier, Jean & Michel, Philippe, 1994. "Discrete-Time Finite Horizon Appromixation of Infinite Horizon Optimization Problems with Steady-State Invariance," Econometrica, Econometric Society, vol. 62(3), pages 635-656, May.
    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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