A numerical scheme for a diffusion equation with nonlocal nonlinear boundary condition
Joydev Halder and Suman Kumar Tumuluri
在这篇文章中,介绍了一个数值方案,以找到具有扩散(M-V-D)的McKendrick-Von Foerster方程的近似解。 使用标准分析来研究此方案的性质的主要困难是由于在M-V-D中的Robin边界条件下存在非线性和非局部术语。 为了克服这一点,我们使用基于稳定性阈值概念的离散化理论来分析方案。 建立了稳定性和拟议的数字方案的趋同。
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 pro...