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On Potentialized Partial Finite Difference Equations: Analyzing The Complexity Of Knowledge-Based Spatial Economic Developments


  • Bernard COUTROT

    () (Université de Bretagne Sud, France)

  • Jean H.P. PAELINCK

    () (George Mason University, School of Public Policy, USA)

  • Alain SALLEZ

    () (Professor Emeritus, ESSEC, Paris)

  • Ryan SUTTER

    () (George Mason University, School of Public Policy, USA)


Knowledge-based regional and urban studies are plentiful; some systematics might be in order at this junction, so first the different links between economic production units in geographical space have to be clearly defined. Then a tool to represent the dynamics of those links should be selected; potentialized partial differential equations (PPDEs) are an appropriate tool to represent space-time relations in pre-geographical space. In practice, however, only discrete data are available, hence the question of how finite differences could generate PPFDEs (potentialized partial finite difference equations). A case has been worked out and simulated, showing a high degree of spatio-temporal complexity. Spatial econometric estimation is possible, as other work has shown; so an application to empirical data for France could be presented. Different versions of the latter have been worked out; they are presented in succession, followed by a last exercise on US data.

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  • Bernard COUTROT & Jean H.P. PAELINCK & Alain SALLEZ & Ryan SUTTER, 2009. "On Potentialized Partial Finite Difference Equations: Analyzing The Complexity Of Knowledge-Based Spatial Economic Developments," Region et Developpement, Region et Developpement, LEAD, Universite du Sud - Toulon Var, vol. 29, pages 237-264.
  • Handle: RePEc:tou:journl:v:29:y:2009:p:237-264

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    References listed on IDEAS

    1. Paelinck, J., 1978. "Spatial econometrics," Economics Letters, Elsevier, vol. 1(1), pages 59-63.
    2. Jean Paelinck, 2000. "Controlling Complexity in Spatial Modelling," CESifo Working Paper Series 362, CESifo Group Munich.
    3. Johan F. Kaashoek & Jean H. P. Paelinck, 2001. "Potentialised partial differential equations in spatial economics: Some further results on the potentialising function," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 35(3), pages 463-482.
    4. Riccardo Leoncini & Sandro Montresor, 2003. "Technological Systems and Intersectoral Innovation Flows," Books, Edward Elgar Publishing, number 2402.
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    Cited by:

    1. Paelinck, Jean H. P., 2011. "On Some Analytical Statistics for Geographic Patterns: From Non-linearity to Linearity," INVESTIGACIONES REGIONALES - Journal of REGIONAL RESEARCH, Asociación Española de Ciencia Regional, issue 21, pages 11-18.

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    JEL classification:

    • F13 - International Economics - - Trade - - - Trade Policy; International Trade Organizations
    • F15 - International Economics - - Trade - - - Economic Integration
    • Q17 - Agricultural and Natural Resource Economics; Environmental and Ecological Economics - - Agriculture - - - Agriculture in International Trade


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