Finite difference schemes to a mathematical model for tumour invasion(Mathematical Medicine, Special Issue on "Joint Symposium of JSIAM Activity Groups 2007")

Abstract

The purpose of this paper is to consider finite difference schemes to a mathematical model for tumour invasion. This mathematical model has two important properties. One is conservation of mass, the other is conservation of the positivity. But the standard discretization destroys these properties. In order to overcome this issue, we construct finite difference scheme satisfying these properties by upwind technique.