On the numerical solution to a Solow model with spatial diffusion and technology-induced capital mobility
This work studies a parabolic-parabolic PDE system that describes the evolution of physical capital (denoted by ”k”) and technological progress (denoted by ”A”). The study employs a meshless method in one and two- dimensional bounded domains with regular boundaries. The well-known Solow model is ext...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universidad Nacional de Educación a Distancia |
| Repositorio: | e-spacio. Repositorio Institucional de la UNED |
| Idioma: | inglés |
| OAI Identifier: | oai:e-spacio.uned.es:20.500.14468/24953 |
| Acceso en línea: | https://hdl.handle.net/20.500.14468/24953 |
| Access Level: | acceso abierto |
| Palabra clave: | 12 Matemáticas::1206 Análisis numérico 53 Ciencias Económicas::5305 Sistemas económicos::5305.01 Sistemas económicos capitalistas Solow model Generalized Finite Difference Meshless method Parabolic PDEs |
| Sumario: | This work studies a parabolic-parabolic PDE system that describes the evolution of physical capital (denoted by ”k”) and technological progress (denoted by ”A”). The study employs a meshless method in one and two- dimensional bounded domains with regular boundaries. The well-known Solow model is extended to consider the spatial diffusion of both capital and technology. Additionally, we study the case in which induced movement of capital towards regions with a large technological progress occurs. For such models, we propose schemes based on the Generalized Finite Difference method and prove the convergence of the numerical solution to the continuous one, which is the main objective of the study. Several examples show the dynamics of the model for a wide range of parameters, illustrating the accuracy of the numerical method. |
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