Niazkar, MajidTurkkan, Gokcen Eryilmaz2024-10-042024-10-0420211687-91201687-9139https://doi.org/10.1155/2021/6692067http://hdl.handle.net/20.500.12403/3010In this study, twenty-two new mathematical schemes with third-order of convergence are gathered from the literature and applied to pipe network analysis. The presented methods were classified into one-step, two-step, and three-step schemes based on the number of hypothetical discharges utilized in solving pipe networks. The performances of these new methods and Hardy Cross method were compared by solving a sample pipe network considering four different scenarios (92 cases). The results show that the one-step methods improve the rate of convergence of the Hardy Cross method in 10 out of 24 cases (41%), while this improvement was found to be 39 out of 56 cases (69.64%) and 5 out of 8 cases (62.5%) for the two-step and three-step methods, respectively. This obviously indicates that the modified schemes, particularly the three-step methods, improve the performance of the original loop corrector method by taking lower number of iterations with the compensation of relatively more computational efforts.eninfo:eu-repo/semantics/openAccessArticle202110.1155/2021/66920672-s2.0-85103031914Q3WOS:000631920800002Q3