Two positivity preserving flux limited,second‐order numerical methods for a haptotaxis model

Two numerical methods for a one‐dimensional haptotaxis model, which exploit the use of van Leer flux limiter, are developed and analyzed. Sufficient conditions time step size and flux limiting are given for such formulation to ensure the non‐negativity of the discrete solution and second‐order accuracy in space. Another advantage is that we avoid solving large nonlinear systems of algebraic equations. The discrete preservation of total conservation of cell density, concentration, and logarithmic density is also verified for the numerical solution. Numerical results concerning accuracy, convergence rate, positivity, and conservation properties are presented and discussed. Similar approach could be applied efficiently in the corresponding two‐ and three‐dimensional problems. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2013