On the use of Simpson's rule in renal models

SUMMARYTwo numerical methods for solving two-point boundary-value problems associated with systems of first-order nonlinear ordinary differential equations are described. The first method, which is based on Lobatto quadrature, requires four internal function evaluations for each subinterval. It does not need derivatives and is of order h7, where h is the space chop. The second method, which is similar to the first but is based on Lobatto-Hermite quadrature, makes the additional use of derivatives to achieve O( h9) accuracy. Results of computational experiments comparing these methods with other known methods are given.

show abstract

Urinary Concentration and Dilution: Models

Stephenson

1992

Comprehensive Physiology

View full text Add to dashboard Cite

The sections in this article are: Whole‐Body Water and Solute Balance Osmolal Clearance Effect on Plasma Osmolality of Urine Flow of a Given Osmolality Hypertonic Urine Implies a Hypotonic Tubular Reabsorbate and Vice Versa Free Water Clearance Antidiuretic Hormone Controls Water Excretion Functional Implications of Renal Architecture Production of Hyperosmotic Urine Is Related to the Loop of Henle Significance of the S‐Shaped Configuration of the Mammalian Nephron for the Concentration of Urine New Functional Features Introduced by the S‐Shaped Configuration A Short History of Models of the Renal Counterflow System Active Water Transport Concentration by Differential Permeabilities and Counterflow Concentration by Multiplication of a “Single Effect” along the Loop of Henle Active Salt Transport out of the AHL Is the Probable Single Effect Experimental Predictions of the Kuhn Models Problems with the Kuhn Models Vasa Recta Models Nephrovascular Models Equations for the Renal Medulla Differential Equations Integrated Mass Balance Equations Generalized Multiplication Rule Nephrovascular Coupling Transmural Fluxes Analytical Solution of the Differential Equations Solutions for Single Flow Tubes Analytical Solutions of Multitube Counterflow Problems Solutions for Central Core Model Externally Driven Central Core Multiplier Multiplication in Inner and Outer Medullae Non‐Zero Diffusion Coefficient Solution of Time‐Dependent Equations Numerical Solution of the Differential Equations Method of Lines Shooting Method Quasilinearization Finite Difference Methods Results of Computer Simulation Origin of Inner Medullary Concentration Gradient Role of Collecting Duct Role of Vasa Recta Transition from Diuresis to Antidiuresis Free‐Energy Balance in Renal Counterflow Systems Summary and Future Directions

show abstract

On the use of Simpson's rule in renal models

Cited by 12 publications

References 7 publications

Improving the accuracy of finite difference methods for solving boundary value ordinary differential equations

Improving the accuracy of finite difference methods for solving boundary value ordinary differential equations

Two high‐order numerical methods for solving boundary‐value nonlinear ordinary differential equations

Urinary Concentration and Dilution: Models

Contact Info

Product

Resources

About