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Numerical solution to a Parabolic-ODE Solow model with spatial diffusion and technology-induced motility

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  • Nicol'as Ure~na
  • Antonio M. Vargas

Abstract

This work studies a parabolic-ODE PDE's system which describes the evolution of the physical capital "$k$" and technological progress "$A$", using a meshless in one and two dimensional bounded domain with regular boundary. The well-known Solow model is extended by considering the spatial diffusion of both capital anf technology. Moreover, we study the case in which no spatial diffusion of the technology progress occurs. For such models, we propound schemes based on the Generalized Finite Difference method and proof the convergence of the numerical solution to the continuous one. Several examples show the dynamics of the model for a wide range of parameters. These examples illustrate the accuary of the numerical method.

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  • Nicol'as Ure~na & Antonio M. Vargas, 2024. "Numerical solution to a Parabolic-ODE Solow model with spatial diffusion and technology-induced motility," Papers 2402.02197, arXiv.org.
    • Handle: RePEc:arx:papers:2402.02197
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    References listed on IDEAS

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    1. Boucekkine, Raouf & Camacho, Carmen & Zou, Benteng, 2009. "Bridging The Gap Between Growth Theory And The New Economic Geography: The Spatial Ramsey Model," Macroeconomic Dynamics, Cambridge University Press, vol. 13(1), pages 20-45, February.
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