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

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

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

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.

Original languageEnglish (US)
JournalThe American journal of physiology
Volume251
Issue number2 Pt 2
StatePublished - Aug 1986
Externally publishedYes

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Automatic derivative evaluation in solving boundary value problems : the renal medulla. / Wexler, A. S.; Kalaba, R. E.; Marsh, D. J.

In: The American journal of physiology, Vol. 251, No. 2 Pt 2, 08.1986.

Research output: Contribution to journalArticle

Wexler, A. S. ; Kalaba, R. E. ; Marsh, D. J. / Automatic derivative evaluation in solving boundary value problems : the renal medulla. In: The American journal of physiology. 1986 ; Vol. 251, No. 2 Pt 2.
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