IMI Interdisciplinary Mathematics InstituteCollege of Arts and Sciences

Ninth Annual Graduate Student Mini-conference in Computational Mathematics

Shuang Liu
University of South Carolina
Abstract

Numerical methods for a class of reaction-diffusion equations with free boundaries

  • Feb. 18, 2018
  • 10:40 a.m.
  • LeConte 412

The systems of reaction-diffusion equations coupled with moving boundaries defined by Stefan condition have been widely used to describe the dynamics of spreading population. There are several numerical difficulties to efficiently handle such systems. We introduce a front tracking method coupled with implicit solver for 1D model as well as a 2D system with radial symmetry to overcome the difficulties. For the general 2D model, we apply level set approach to handle the moving boundaries to efficiently treat complicated topological changes. The numerical examples are performed to illustrate the efficiency, accuracy and consistency for different approaches.

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