AN ADI METHOD FOR HYSTERETIC REACTION-DIFFUSION SYSTEMS

In this paper we consider a mathematical model motivated by patterned growth of bacterial cells. The model is a system of differential equat ions that consists of two subsystems. One is a system of ordinary diff erential equations and the other is a reaction-diffusion system. An al ternating-direction implicit (ADI) method is derived for numerically s olving the system. The ADI method given here is different from the usu al ADI schemes for parabolic equations due to the special treatment of nonlinear reaction terms in the system. Stability and convergence of the ADI method are proved. We apply these results to the numerical sol ution of a problem in microbiology.