A monotone conservative Eulerian–Lagrangian scheme for reaction‐diffusion‐convection equations modeling chemotaxis

A numerical method for convection dominated diffusion problems, that exploits the use of characteristics, is derived and analyzed. It is shown to preserve positivity of solutions and be locally mass conserving. Stability, consistency and order one convergence are verified. Because of the way in which it determines characteristic pre-images of grid cells, the method can be easily implemented for 1-, 2-, or 3-dimensional problems on rectangular grids.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007