1985
DOI: 10.1016/0010-4825(85)90012-5
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On the solution of equations for renal counterflow models

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Cited by 19 publications
(3 citation statements)
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“…If we consider tube j to be divided into n slices, then the spacecentered finite difference equations between nodes k-1 and k are where i represents flows of volume, NaCl, urea, glucose, or lactate. Thus the fluxes J i j are evaluated at the middle of the interval ["midpoint method" (38)], on the assumption that concentrations in the middle of the interval are the arithmetic average of the concentrations at k-1 and k.…”
Section: Numerical Solutionmentioning
confidence: 99%
“…If we consider tube j to be divided into n slices, then the spacecentered finite difference equations between nodes k-1 and k are where i represents flows of volume, NaCl, urea, glucose, or lactate. Thus the fluxes J i j are evaluated at the middle of the interval ["midpoint method" (38)], on the assumption that concentrations in the middle of the interval are the arithmetic average of the concentrations at k-1 and k.…”
Section: Numerical Solutionmentioning
confidence: 99%
“…In the most numerical methods, Newton-based methods [2] [13] [14] and quasilinearization in conjunction with a Newton-type solver [4] [15] have been used to solve the steady-state model of urine concentrating mechanism. However, these methods have difficulties with numerical instability which arises from reversal intratubular flow relative to the assumed steady-state direction [16].…”
Section: Introductionmentioning
confidence: 99%
“…The method is based on splines as trial funetions for these concentrations and on collocation of the central-core equations (23). Once these trial funetions are given, the tubule equations and boundary conditions form a sequence of initial-value problems (each in the corresponding direction of flow).…”
mentioning
confidence: 99%