2023/12/12 by Huong Luu, Luu, Huong, Marek Chrobák +1
Computer Science · Engineering · Mathematics · #Computational Engineering #FOS: Computer and information sciences #Finance #Fractional Differential Equations Solutions #Image and Signal Denoising Methods #Water Systems and Optimization #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2312.07681
openalex publication_date 2023/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Analysis of pipe networks involves computing flow rates and pressure differences on pipe segments in the network, given the external inflow/outflow values. This analysis can be conducted using iterative methods, among which the algorithms of Hardy Cross and Newton-Raphson have historically been applied in practice. In this note, we address the mathematical analysis of the local convergence of these algorithms. The loop-based Newton-Raphson algorithm converges quadratically fast, and we provide estimates for its convergence radius to correct some estimates in the previous literature. In contrast, we show that the convergence of the Hardy Cross algorithm is only linear. This provides theoretical confirmation of experimental observations reported earlier in the literature.