Numerical methods for three-dimensional models of the urine concentrating mechanism

Anthony S. Wexler, Donald J. Marsh

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We recently formulated and solved a successful model of the renal concentrating mechanism, a problem of long-standing interest in mathematical biology [33, 34]. The model is a 39th-order nonlinear two-point boundary-value problem with separated linear boundary conditions. Although quasilinearization and superposition with Gram-Schmidt orthonormalization successfully solved the equations, these methods will probably not be sufficient to solve more detailed models of the urine concentrating mechanism. In this paper we review the current literature on solving two-point boundary-value problems and find a number of promising alternatives and improvements to our current methods. In addition we derive a new numerical method for calculating the parameter sensitivity of the solution to a nonlinear two-point boundary-value problem coupled to a system of algebraic relations. This new method is faster and more accurate than the method previously employed.

Original languageEnglish (US)
Pages (from-to)219-240
Number of pages22
JournalApplied Mathematics and Computation
Volume45
Issue number2
DOIs
StatePublished - 1991
Externally publishedYes

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Boundary value problems
Numerical methods
Two-point Boundary Value Problem
Numerical Methods
Three-dimensional
Nonlinear Boundary Value Problems
Mathematical Biology
Quasilinearization
Parameter Sensitivity
Boundary conditions
Model
Superposition
Sufficient
Alternatives

ASJC Scopus subject areas

  • Applied Mathematics
  • Computational Mathematics
  • Numerical Analysis

Cite this

Numerical methods for three-dimensional models of the urine concentrating mechanism. / Wexler, Anthony S.; Marsh, Donald J.

In: Applied Mathematics and Computation, Vol. 45, No. 2, 1991, p. 219-240.

Research output: Contribution to journalArticle

Wexler, Anthony S. ; Marsh, Donald J. / Numerical methods for three-dimensional models of the urine concentrating mechanism. In: Applied Mathematics and Computation. 1991 ; Vol. 45, No. 2. pp. 219-240.
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