In this article, a numerical scheme to find approximate solutions to the McKendrick-Von Foerster equation with diffusion (M-V-D) is presented. The main difficulty in employing the standard analysis to study the properties of this scheme is due to presence of nonlinear and nonlocal term in the Robin boundary condition in the M-V-D. To overcome this, we use the abstract theory of discretizations based on the notion of stability threshold to analyze the scheme. Stability, and convergence of the proposed numerical scheme are established.
翻译:文章中提出了一个数字办法,用扩散法(M-V-D)来寻找McKindrick-Von Foerster等式的近似解决办法,使用标准分析来研究这一办法的特性的主要困难在于,在M-V-D.的Robin边界条件中存在非线性和非本地性术语。 为解决这一问题,我们利用基于稳定门槛概念的抽象离散理论来分析这一办法。确定了拟议数字办法的稳定性和趋同性。