Numerical Analysis of Tumor Model in Steady State

In this paper we study the numerical approximation of the steady state tumor model proposed by Chaplain and Stuart [1] to describe the angiogenesis process through which new blood vessels are produced. The existence and convergence properties of finite difference approximation solutions are shown. More precisely, we also show that this numerical scheme preserves the structure properties earlier established for the analytical model. Furthermore we actually obtain improvements on the structure conditions given in [2]. Some numerical examples are also carried out to demonstrate our theoretical justifications.