Convergence of Newton method in nonlinear network analysis
type: Item
instance of: scholarly article
title: Convergence of Newton method in nonlinear network analysis
zbMATH Open document ID: 0824.65030
DOI: 10.1016/0895-7177(95)00004-L
published in: Mathematical and Computer Modelling
publication date: 1995-10-22T00:00:00Z
review text: Newton methods for hydraulic network analysis based on the unknown edge flow rates (flow method), corrected loop flow rates (loop method) and nodal heads or pressures (nodal method) were proposed by a number of researchers. Convergence problems were frequently observed with the nodal formulation. Two of the most important convergence difficulties encountered were attributed to edges with relatively low resistances and to improper selection of initial nodal head values. In the paper the convergence conditions of Newton methods for the three network analysis formulations are examined. Based on the estimation of the magnitude of the radius of attraction for Newton method, it indicates that the flow and loop formulations give better convergence than the nodal head or pressure formulation.
Mathematics Subject Classification ID: 65H10
zbMATH DE Number: 751283
zbMATH Keywords: nonlinear hydraulic network
zbMATH Keywords: network flow
zbMATH Keywords: flow method
zbMATH Keywords: loop method
zbMATH Keywords: nodal method
zbMATH Keywords: convergence
zbMATH Keywords: Newton methods
zbMATH Keywords: hydraulic network analysis
zbMATH Keywords: radius of attraction
author: Tom Altman
author: Paul F. Boulos
reviewed by: Cheng-Xian Xu
MaRDI profile type: Publication
cites work: Inverse formulation and finite difference solution for flow from a circular orifice
cites work: Method of steady-state simulation of a gas network
cites work: A graph-theoretic approach to explicit nonlinear pipe network optimization
cites work: Q5332416
description: scientific article; zbMATH DE number 751283