Fractional step methods applied to a chemotaxis model

A fractional step numerical method is developed for the nonlinear partial d ifferential equations arising in chemotaxis models, which include density-d ependent diffusion terms for chemotaxis, as well as reaction and Fickian di ffusion terms. We take the novel approach of viewing the chemotaxis term as an advection term which is possible in the context of fractional steps. Th is method is applied to pattern formation problems in bacterial growth and shown to give good results, High-resolution methods capable of capturing st eep gradients (from CLAWPACK) are used for the advection step, while the A- stable and L-stable TR-BDF2 method is used fur the diffusion step. A numeri cal instability that is seen with other diffusion methods is analyzed and e liminated.