Numerical Methods for Reaction-Diffusion Equations and the Application in Computational Biology

When
Start: 10/23/2017 - 4:15pm
End  : 10/23/2017 - 5:15pm

Category
Applied Math Seminar

Speaker
Weitao Chen (UCR)

Abstract

Reaction-diffusion equations have wide applications in natural and engineering sciences. The efficiency of numerical methods for these equations is often limited by the severe stability conditions due to diffusion and stiff reactions, as well as the curse of dimensionality for equations in high-dimensional spaces. We developed a numerical method to improve the efficiency by relaxing stability constraints, coupled with sparse grid technique, for solving reaction-diffusion equations in high dimensions. We also extend this method to more general systems with nonhomogeneous boundary conditions or explicitly time-dependent reactions. In addition, I will introduce its application in modeling a complex biological system, the macropatterning in mouse tongue, to understand the robustness strategies in pattern formation on a growing tissue.

Where
Emmy Noether Rm, Millikan 1021, Pomona College