论文标题
与非本地边界条件的抛物线方程的收敛数值方案
A convergent numerical scheme to a parabolic equation with a nonlocal boundary condition
论文作者
论文摘要
在本文中，提出了具有Dirichlet边界条件的非线性McKendrick-von foerster方程的数值方案。得出该方案的主要思想是根据对流部分的特征方法使用离散化，以及对对流的有限差方法。非本地术语涉及正交方法。结果，对于正在考虑的边界价值问题，获得了隐式方案。建立了所提出的数值方案的一致性和收敛性。此外，提出了数值模拟以验证理论结果。
In this paper, a numerical scheme for a nonlinear McKendrick-von Foerster equation with diffusion in age (MV-D) with the Dirichlet boundary condition is proposed. The main idea to derive the scheme is to use the discretization based on the method of characteristics to the convection part, and the finite difference method to the rest of the terms. The nonlocal terms are dealt with the quadrature methods. As a result, an implicit scheme is obtained for the boundary value problem under consideration. The consistency and the convergence of the proposed numerical scheme is established. Moreover, numerical simulations are presented to validate the theoretical results.
