Pointwise solution bounds for a class of singular diffusion problems in physiology

摘要

A numerical technique for obtaining pointwise bounds for the solution of a class of nonlinear boundary-value problems in physiology is presented. Simple analytic bounding functions are obtained using an integral representation for the solution. The computations are performed in interval arithmetic, thus obtaining lower and upper bounds simultaneously. The oxygen diffusion problem in spherical cells and a nonlinear heat-conduction model of the human head are presented as illustrative examples. For these examples, the present technique is computationally more efficient than the existing ones in that it yields sharper bounds with fewer integration steps.