Computation of traveling wave fronts for a nonlinear diffusion-advection model - M. B. A. Mansour (Mathematical Biosciences and Engineering)
This paper utilizes a nonlinear reaction-diffusion-advection modelfor describing the spatiotemporal evolution of bacterial growth. Thetraveling wave solutions of the corresponding system of partialdifferential equations are analyzed. Using two methods, we then findsuch solutions numerically. One of the methods involves thetraveling wave equations and solving an initial-value problem, whichleads to accurate computations of the wave profiles and speeds. Thesecond method is to construct time-dependent solutions bysolving an initial-moving boundary-value problem for the PDE system,showing another approximation for such wave solutions.