Convergence of Newton method in nonlinear network analysis
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.
scientific article; zbMATH DE number 751283