Piller, O.Elhay, S.Deuerlein, J.W.Simpson, A.R.2025-06-252025-06-252024Engineering Proceedings, 2024, vol.69, iss.1, pp.165-1-165-52673-4591https://hdl.handle.net/2440/145408First-order approximations have been used with some success for criticality analysis; sensitivity analysis of physical networks, such as water distribution systems; and uncertainty propagation of model parameters. Certain limitations have been reported regarding the accuracy of the results, particularly when non-linearity is dominant. In this paper, we show how to efficiently derive the first- and second-order sensitivities with respect to variation in their parameters. This makes it possible to improve the first-order estimate when necessary. The method is illustrated on a small example system.en© 2024 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).sensitivities; Schur complement; linear equations; sparse matrix; steady state: demanddriven modeling; pressure-driven modeling; water distribution systemsConference paper10.3390/engproc2024069165710650Piller, O. [0000-0002-3625-7639]Elhay, S. [0000-0003-3440-556X]Simpson, A.R. [0000-0003-1633-0111]