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(infinity)-norm for many cases.
Title
A Stable Algorithm for Non-Negative Invariant Numerical Solution of Reaction-Diffusion Systems on Complicated Domains
Published
2012-05-10
Full Collection Name
Electrical Engineering & Computer Sciences Technical Reports
Other Identifiers
EECS-2012-77
Type
Text
Extent
52 p
Archive
The Engineering Library
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