References
- Ascher U. M., Petzold L. R. (1998) Computer methods for Ordinary Differential Equations and Difference-Algebraic Equations, SIAM, Philadelphia.10.1137/1.9781611971392
- Artichowicz W., Szymkiewicz R. (2014) Computational issues of solving the 1D steady gradually varied flow equation, J. Hydrol. Hydromech., 62 (3), 226–233, DOI: 10.2478/johh-2014-0031.10.2478/johh-2014-0031
- Artichowicz, W., Mikos-Studnicka, P. (2014) Comparison of Average Energy Slope Estimation Formulas for One-dimensional Steady Gradually Varied Flow, Archives of Hydro-Engineering and Environmental Mechanics, 61 (3–4), 89–109, DOI: 10.1515/heem-2015-000610.1515/heem-2015-0006
- Chanson H. (2004) The hydraulics of open channel flow: an introduction. Second Edition. Elsevier.10.1016/B978-075065978-9/50006-4
- Chadderton R. A., Miller A. C. (1980) Friction models for M2 profiles, JAWRA Journal of the American Water Resources Association, 16 (2), 235–242, DOI: 10.1111/j.1752-1688.1980.tb02384.x.10.1111/j.1752-1688.1980.tb02384.x
- Cunge J. A., Holly F. M., Verwey A. (1979) Practical aspects of computational river hydraulics, Pitman advanced publishing program, Boston, London, Melbourne.
- Chow V. T. (1959) Open-channel hydraulics, McGraw-Hill / Kogakusha Company LTD, Tokyo.
- Fatunla S. O. (1982) Nonlinear multistep methods for initial value problems, Computers&Mathematics with Applications, 8 (3), 231–239, DOI: 10.1016/0898-1221(82)90046-3.10.1016/0898-1221(82)90046-3
- French R. H. (1985) Open Channel Hydraulics, McGraw-Hill, New York.
- Gustafsson B. (2011) Fundamentals of Scientific Computing, Springer-Verlag, Berlin, Heidelberg.
- Gasiorowski D. (2013) Impact of diffusion coefficient averaging on solution accuracy of the 2D nonlinear diffusive wave equation for floodplain inundation, Journal of Hydrology, 517, 923–935, DOI:10.1016/j.jhydrol.2014.06.039.10.1016/j.jhydrol.2014.06.039
- Hairer E., Wanner G. (2010) Solving Ordinary Differential Equations II. Stiff and Differential-Algebraic Problems, Second Revised Edition, Springer, Berlin, Heidelberg.
- Kincaid D., Cheney W. (2002) Numerical Analysis, Wydawnictwa Naukowo-Techniczne, Warszawa (in Polish).
- Lambert J. D., Shaw B. (1965) A Method for Numerical Solution of y′ = f (x, y) Based on a Self-Adjusting Non-Polynomial Interpolant, Math. Comp., 20, 11–20, DOI: 10.1090/S0025-5718-1966-0189252-1.10.1090/S0025-5718-1966-0189252-1
- Laurenson E. M. (1986) Friction Slope Averaging in Backwater Calculations, J. Hydraul. Eng., 112 (12), 1151–1163.10.1061/(ASCE)0733-9429(1986)112:12(1151)
- LeVeque R. J. (2007) Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, DOI:10.1137/1.9780898717839.10.1137/1.9780898717839
- Luke Y. L., Fair W., Wimp J. (1975) Predictor-corrector formulas based on rational interpolants., Computers & Mathematics with Applications, 1 (1), 3–12, DOI: 10.1016/0898-1221(75)90003-6.10.1016/0898-1221(75)90003-6
- MacDonald I., Baines M. J., Nichols N. K., Samuels P. G. (1997) Analytic Benchmark Solutions for Open-Channel Flows, J. Hydraul. Eng., 123 (11), 1041–1045.10.1061/(ASCE)0733-9429(1997)123:11(1041)
- Szymkiewicz R. (2010) Numerical modeling in open channel hydraulics, Springer.10.1007/978-90-481-3674-2
- US Army Corps of Engineers (2010) HEC-RAS hydraulic reference.