The method of lines for the numerical solution of a mathematical model in the initiation of angiogenesis

Abstract

In this paper we present the method of lines to obtain the numerical solution of a mathematical model for the roles of endothelial, pericyte and macrophage cells in the initiation of tumor angiogenesis. This method is an approach to the numerical solution of partial differential equations that involve a time variable t and a space variable x. We provide computer programs written in Matlab. Also, the stability analysis of the solutions is given, and the figures for endothelial, pericyte and macrophage cell movements in the capillary are presented for large times.