An efficient implementation of a numerical method for a chemotaxis system

Abstract

A system of partial differential equations modelling the attraction of a population of cells to a biochemical concentration in its environment is considered. The system incorporates convective and diffusive effects, either of which may dominate. A numerical method is presented that allows for both possible features, which conserves positivity of solutions and their mass in the absence of sources or sinks. An efficient implementation of the method in a two-dimensional setting is described that uses fast Poisson solvers for either 5- or 9-pt stencils approximating the Laplacian. It is also shown that the computational work for either stencil is essentially the same.

Keywords:

• chemotaxis
• convection
• diffusion
• 9-pt stencil
• fast Poisson solver

2000 AMS Subject Classification :

• 65M06
• 65M12
• 65M25

Acknowledgements

This work has been partially supported by the National Institutes of Health under contract grant number R01 GM072005-01.