On the numerical solution to a Solow model with spatial diffusion and technology-induced capital mobility

Abstract

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.