Math @ Duke

Publications [#287298] of Harold Layton
Papers Published
 Pitman, EB; Layton, HE, Mass conservation in a dynamic numerical method for a model of the urine concentrating mechanism,
ZammZeitschrift Fuer Angewandte Mathematik Und Mechanik, vol. 76 no. SUPPL. 4
(1996),
pp. 4548, ISSN 00442267
(last updated on 2018/05/27)
Abstract: Dynamic models of the urine concentrating mechanism consist of large systems of hyperbolic partial differential equations (PDEs), expressing solute conservation, coupled to ordinary differential equations (ODEs) for water conservation. Most numerical methods reformulate these equations in the steadystate, yielding boundaryvalue systems of stiff ODEs, which are usually solved by some variant of Newton's method. We have developed an explicit, secondorder numerical method for solving the dynamic PDEODE system. The method is robust and easily adapted to different renal architectures. Moreover, as we show here, when the method is used in a largescale simulation of the renal medulla, the asymptotic steadystate exhibits secondorder spatial convergence in solute and water mass flows.


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