Electrical Engineering
      and Computer Sciences

Electrical Engineering and Computer Sciences

COLLEGE OF ENGINEERING

UC Berkeley

A Stable Algorithm for Non-Negative Invariant Numerical Solution of Reaction-Diffusion Systems on Complicated Domains

Insoon Yang

EECS Department
University of California, Berkeley
Technical Report No. UCB/EECS-2012-77
May 10, 2012

http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-77.pdf

We present a Cartesian grid finite difference numerical method for solving a system of reaction-diffusion initial boundary value problems with Neumann type boundary conditions. The method utilizes adaptive time-stepping, which guarantees stability and non-negativity of the solutions. The latter property is critical for models in biology where solutions rep- resent physical measurements such as concentration. The level set representation of the boundary enables us to handle domains with complicated geometry with ease. We pro- vide numerical validation of our method on synthetic and biological examples. Empirical tests demonstrate second order convergence rate in the L1- and L2-norms, as well as in the L∞-norm for many cases.

Advisor: Claire Tomlin


BibTeX citation:

@mastersthesis{Yang:EECS-2012-77,
    Author = {Yang, Insoon},
    Title = {A Stable Algorithm for Non-Negative Invariant Numerical Solution of Reaction-Diffusion Systems on Complicated Domains},
    School = {EECS Department, University of California, Berkeley},
    Year = {2012},
    Month = {May},
    URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-77.html},
    Number = {UCB/EECS-2012-77},
    Abstract = {We present a Cartesian grid finite difference numerical method for solving a system of reaction-diffusion initial boundary value problems with Neumann type boundary conditions. The method utilizes adaptive time-stepping, which guarantees stability and non-negativity of the solutions. The latter property is critical for models in biology where solutions rep- resent physical measurements such as concentration. The level set representation of the boundary enables us to handle domains with complicated geometry with ease. We pro- vide numerical validation of our method on synthetic and biological examples. Empirical tests demonstrate second order convergence rate in the L1- and L2-norms, as well as in the L∞-norm for many cases.}
}

EndNote citation:

%0 Thesis
%A Yang, Insoon
%T A Stable Algorithm for Non-Negative Invariant Numerical Solution of Reaction-Diffusion Systems on Complicated Domains
%I EECS Department, University of California, Berkeley
%D 2012
%8 May 10
%@ UCB/EECS-2012-77
%U http://www.eecs.berkeley.edu/Pubs/TechRpts/2012/EECS-2012-77.html
%F Yang:EECS-2012-77