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Multidimensional Transitional Dynamics: A Simple Numerical Procedure (Matlab)


  • Timo Trimborn

    (University of Hannover)

  • Karl-Joseph Koch

    (University of Siegen)

  • Thomas Steger

    (University of Leipzig)


Programs for the method proposed in the article. We propose the relaxation algorithm as a simple and powerful method for determining the transition process in growth models numerically. This method has a number of important advantages: (1) It can easily deal with a wide range of dynamic systems including stiff differential equations and systems giving rise to a continuum of stationary equilibria. (2) The application of the procedure is fairly user-friendly. The only input required consists of the dynamic system. (3) The variant of the relaxation algorithm we propose exploits in a natural manner the infinite time horizon, which usually underlies optimal control problems in economics. As an illustrative application, we compute the transition process of the models of Jones (1995) and Lucas (1988).

Suggested Citation

  • Timo Trimborn & Karl-Joseph Koch & Thomas Steger, 2008. "Multidimensional Transitional Dynamics: A Simple Numerical Procedure (Matlab)," QM&RBC Codes 194, Quantitative Macroeconomics & Real Business Cycles.
  • Handle: RePEc:dge:qmrbcd:194

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    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • O40 - Economic Development, Innovation, Technological Change, and Growth - - Economic Growth and Aggregate Productivity - - - General


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