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 language | English (US) |
|---|---|
| Journal | The American journal of physiology |
| Volume | 251 |
| Issue number | 2 Pt 2 |
| State | Published - Aug 1986 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Medicine(all)
Cite this
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 journal › Article
}
TY - JOUR
T1 - Automatic derivative evaluation in solving boundary value problems
T2 - the renal medulla.
AU - Wexler, A. S.
AU - Kalaba, R. E.
AU - Marsh, D. J.
PY - 1986/8
Y1 - 1986/8
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=18544409640&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=18544409640&partnerID=8YFLogxK
M3 - Article
C2 - 3740280
AN - SCOPUS:18544409640
VL - 251
JO - American Journal of Physiology - Renal Fluid and Electrolyte Physiology
JF - American Journal of Physiology - Renal Fluid and Electrolyte Physiology
SN - 1931-857X
IS - 2 Pt 2
ER -