The method of lines for the numerical solution of a mathematical model for capillary formation: The role of endothelial cells in the capillary

摘要

In this paper we present the method of lines to obtain the numerical solution of a mathematical model for capillary formation in tumor angiogenesis. This method is an approach to the numerical solution of partial differential equations that involve a time variable t and space variables x, y, … As the number of lines is increased, the accuracy of the method of lines representation of the original system increases. The method provides very accurate numerical solutions for linear and nonlinear problems in comparison with other existing methods. We also provide computer programs written in Matlab and figures that show the endothelial cell movement.