  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.
