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Am J Physiol Renal Physiol 251: F358-F378, 1986;
0363-6127/86 $5.00
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AJP - Renal Physiology, Vol 251, Issue 2 358-F378, Copyright © 1986 by American Physiological Society

ARTICLES

Automatic derivative evaluation in solving boundary value problems: the renal medulla

A. S. Wexler, R. E. Kalaba and D. J. Marsh

Automatic evaluation of derivatives becomes essential when large systems of equations of many variables are to be solved. This paper presents a set of easy-to-use FORTRAN subroutines that perform automatic derivative evaluation. They were used in conjunction with the method of quasilinearization to solve a 13th-order boundary-value problem. This problem has been proposed as a test of numerical methods used to solve models of the renal concentrating mechanism. Quasilinearization gives the same result as has been reported by others with finite difference or multiple shooting methods. The approach described here offers the important potential advantage of being easier to apply to larger problems, which can be anticipated when attempts are made to simulate the three-dimensional structure of the renal medulla.


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A. T. Layton and H. E. Layton
A region-based mathematical model of the urine concentrating mechanism in the rat outer medulla. I. Formulation and base-case results
Am J Physiol Renal Physiol, December 1, 2005; 289(6): F1346 - F1366.
[Abstract] [Full Text] [PDF]


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