A BDF B-spline Method for a Nonlocal Tumor Growth Model

Abstract

This paper presents a model for tumor growth using nonlocal velocity. We establish some results on the existence and uniqueness of the solution for a nonlocal tumor growth model. Many experiences show that tumor spheroid can be invariant by rotation and can guard the shape of the spheroid during the growth process in some particular cases. Here, we assume that the multiple components of the system are invariant by rotation. Then, we use the Backward Differentiation Formula (BDF) spline to solve the nonlocal system. To illustrate the effecienty of the proposed method, we performed numerical tests that simulate a tumor growth scenario. Such techniques may be used to provide informations on practical applications of the model.