SHOOTING METHODS FOR ONE-DIMENSIONAL DIFFUSION-ABSORPTION PROBLEMS

In this paper, a numerical algorithm is presented and analyzed based o n the shooting method to approximate the solution of a model for the d iffusion and absorption of oxygen in living tissue. The model is a var iant of one originally proposed by Crank and Gupta (J. Inst. Math. App l., 10 (1972), pp. 19-33). In that article, the rate of consumption of oxygen is assumed to be constant. In this paper this rate is assumed to be a function of the distance to the outer surface of the tissue. T his allows for an inhomogeneous medium, i.e., the oxygen consumption r ate could vary from point to point.