Accurate computation of traveling wavefronts in a biological hydrodynamic model

Abstract This paper concerns a hyperbolic–elliptic system of partial differential equations for the biological cell density and cell velocity. This system appears as a mathematical model for describing the dynamics of cell motion. Traveling wavefront solutions for the system of equations are computed by using two different numerical methods. One of the methods involves the traveling wave equations and solving an initial-value problem, which leads to accurate computations of the wave profile of cell density and the distributions of the cell velocity. The second method is to solve an initial-moving boundary-value problem for the PDE system, where the traveling wave emerges as the asymptotic long time solution.