Numerical homotopy method for nonlinear PDEs with biological applications

Wenrui Hao
Mathematical Biosciences Institute, The Ohio State University

(October 3, 2013 10:20 AM - 11:15 AM)

Numerical homotopy method for nonlinear PDEs with biological applications

Abstract

This talk will cover some recent progress on numerical homotopy method 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.