Wenrui Hao, University of Notre Dame

Numerical Methods for Nonlinear PDEs with Biological Applications

This talk will cover some recent progress on numerical methods to solve systems of  nonlinear partial differential equations (PDEs) arising from biology and physics.  This new approach, which is used to compute multiple solutions and bifurcation of nonlinear PDEs, makes use of polynomial systems (with thousands of variables) arising by discretization.  Examples from hyperbolic systems, tumor growth models, and a blood clotting model will be used to demonstrate the ideas.