Numerical Approach to Solve Tumor Growth Model With A Free Boundary

We use a new numerical approach, which is based on Numerical Algebraic Geometry, to explore free boundary problems arising from tumor growth models. These methods are used to compute steady state solutions, check their stability, and track the solutions through bifurcations as critical parameters change. The polynomial systems, which involve thousands of variables, pose interesting challenges. This talk will cover the recent progress on a tumor model with PDE, the stability of the solutions, the bifurcation diagram extensions beyond the bifurcation point and the intersection of bifurcation diagram for different bifurcation branch, and possible other types of steady state solutions.