Numerical Modelling of Oxygen Diffusion in Cells with Michaelis-Menten Uptake Kinetics

Journal of Mathematical Chemistry, 48(1) (2010), 145-158
http://dx.doi.org/10.1007/s10910-009-9646-x

A class of singular boundary value problems is studied, which models the oxygen diffusion in a spherical cell with Michaelis-Menten uptake kinetics. Suitable singular Cauchy problems are considered in order to determine one-parameter families of solutions in the neighborhood of the singularities. These families are then used to construct stable shooting algorithms for the solution of the considered problems and also to propose a variable substitution in order to improve the convergence order of the finite difference methods. Numerical results are presented and discussed.