In this paper a parabolic–parabolic chemotaxis system of PDEs that describes the evolution of a population with non-local terms is studied. We derive the discretization of the system using the meshless method called Generalized Finite Difference Method. We prove the conditional convergence of the solution obtained from the numerical method to the analytical solution in the two-dimensional case. Several examples of the application are given to illustrate the accuracy and efficiency of the numerical method. We also present two examples of a parabolic–elliptic model, as generalized by the parabolic–parabolic system addressed in this paper, to show the validity of the discretization of the non-local terms.

本文研究了PDE的抛物线-抛物线趋化系统，该系统描述了具有非局部项的种群的演化。我们使用称为广义有限差分法的无网格方法导出系统的离散化。我们证明了在二维情况下从数值方法获得的解到解析解的条件收敛。给出了几个应用实例来说明数值方法的准确性和效率。我们还给出了抛物线-椭圆模型的两个示例，这些示例由本文讨论的抛物线-抛物线系统推广，以显示非局部项离散化的有效性。