Pointwise solution bounds for a class of singular diffusion problems in physiology
type: Item
instance of: scholarly article
title: Pointwise solution bounds for a class of singular diffusion problems in physiology
zbMATH Open document ID: 0669.92004
DOI: 10.1016/0096-3003(89)90053-2
author: N. S. Asaithambi
author: J. B. Garner
published in: Applied Mathematics and Computation
publication date: 1989-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 92Cxx
Mathematics Subject Classification ID: 92-08
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 65G30
zbMATH DE Number: 4097167
zbMATH Keywords: pointwise bounds
zbMATH Keywords: nonlinear boundary-value problems
zbMATH Keywords: analytic bounding functions
zbMATH Keywords: integral representation
zbMATH Keywords: interval arithmetic
zbMATH Keywords: oxygen diffusion
zbMATH Keywords: spherical cells
zbMATH Keywords: nonlinear heat-conduction model
MaRDI profile type: Publication
full work available at URL: 0096-3003(89)90053-2
OpenAlex ID: W2069579296
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cites work: Q3207999
cites work: Interval mathematics. Proceedings of the international symposium, Karlsruhe, West Germany, May 20-24, 1975
description: scientific article; zbMATH DE number 4097167