Robust numerical method for a tumor-host model with chemotherapy application

Abstract

In this paper, the investigation on a system of time-depended non-linear quasi-parabolic partial differential equations (PPDEs), modeling the chemotherapy application of spatial tumor-host interaction is intensified. The analysis for the continuously dependency of unique solution on the data, local stability analysis of the baseline chemotherapy, anti-angiogenic chemotherapy and cytotoxic chemotherapy dynamics are presented. Since the system of time-dependent non-linear quasi-parabolic partial differential equations cannot be solved analytically, a robust numerical scheme based on the semi-fitted finite difference operator is formulated. Analysis of the basic properties for the method presents that it is consistent, stable and convergent.