Taylor series solution of a class of diffusion problems in physiology

A Taylor series technique for obtaining pointwise bounds for the solution of a class of diffusion problems in physiology is presented. Simple analytic bounding functions are obtained using an integral representation for the solution. Computations are performed in interval arithmetic, and thus lower and upper bounds are obtained simultaneously. Higher-order Taylor coefficients are computed using simple recursion relations. The oxygen diffusion problem in spherical cells is presented as an illustrative example. For this example, the present technique is computationally more efficient than the existing ones in that it yields sharper bounds with fewer integration steps.