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.

翻译：本文研究了一个抛物-常微分方程偏微分方程组，该方程组描述了物理资本"$k$"和技术进步"$A$"的演化过程，采用无网格方法在具有规则边界的一维和二维有界域内进行求解。通过考虑资本与技术的空间扩散效应，对经典的Solow模型进行了拓展。此外，我们还研究了技术进步不发生空间扩散的情形。针对此类模型，我们提出了基于广义有限差分法的数值格式，并证明了数值解收敛于连续解。多个算例展示了模型在广泛参数范围内的动力学行为，这些算例验证了数值方法的准确性。