In this article, for the first time, the least square methods of Gauss-Newton (GN) and Levenberg-
Marquardt (LM) are used for the solution of discharge Q-equations in water distribution networks. The
results are compared with the Newton-Raphson method (NR) and global gradient algorithm, (GGA).
The GGA is used in the current commercial softwares of Water Gems and Epanet. The Newtonian
methods are critically dependent on a suitable initial guess for achieving a desired accuracy to
compete with the GGA. To remove this defect, an algorithm is proposed by linearzing the head-loss
functions. Thereby, the nonlinear energy equations are linearzed and the whole system is solved. The
results are then used as an initial guess for the solution of linear-nonlinear system of discharge-energy
equations. Using this algorithm, it is observed that the rate of convergence in the GN method is much
faster than the GGA and its accuracy is higher.