J. S. Gulliver, Introduction to chemical transport in the environment. Cambridge University Press, 2007.
 S. C. Chapra, Surface Water-Quality Modeling, McGraw-Hill Publisher. New York, 1997.
 M. Mazaheri, J. Mohammad Vali Samani, and H. M. V. Samani, “Mathematical Model for Pollution Source Identification in Rivers,” Environ. Forensics, Vol. 16, pp. 310-321, 2015.
 Nardo, A.D, Santonastaso, G.F., Battaglia, `R. and Musmarra, D, “Smart identification system of surface water contamination by an innovative biosensor network,” in Conference: CEMEPE - 5th international conference on Environmental Management, Engineering, Planning and Economics, (2015).
 S. Zhang and X. Xin, “Pollutant source identification model for water pollution incidents in small straight rivers based on genetic algorithm,” Appl. Water Sci., vol. 7, no. 4, pp. 1955–1963, 2017.
 M. G. (Kumar) and S. Mohamed, “Hybrid Genetic Algorithm—Local Search Methods for Solving Groundwater Source Identification Inverse Problems,” J. Water Resour. Plan. Manag., vol. 131, no. 1, pp. 45–57, Jan. 2005.
 S. R. Mohan and D. Bithin, “Identification of Groundwater Pollution Sources Using GA-based Linked Simulation Optimization Model,” J. Hydrol. Eng., vol. 11, no. 2, pp. 101–109, Mar. 2006.
 A. Ghane, M. Mazaheri, and J. Mohammad Vali Samani, “Location and release time identification of pollution point source in river networks based on the Backward Probability Method,” J. Environ. Manage., vol. 180, pp. 164–171, 2016.
 W. P. Cheng and Y. Jia, “Identification of contaminant point source in surface waters based on backward location probability density function method,” Adv. Water Resour., vol. 33, no. 4, pp. 397–410, Apr. 2010.
 R. M. Neupauer and J. L. Wilson, “Backward probability model using multiple observations of contamination to identify groundwater contamination sources at the Massachusetts Military Reservation,” Water Resour. Res., vol. 41, no. 2, pp. 1–14, Feb. 2005.
 F. Cupola, M. G. Tanda, and A. Zanini, “Laboratory sandbox validation of pollutant source location methods,” Stoch. Environ. Res. Risk Assess., vol. 29, no. 1, pp. 169–182, 2015.
 J. Wang, J. Zhao, X. Lei, and H. Wang, “New approach for point pollution source identification in rivers based on the backward probability method.,” Environ. Pollut., vol. 241, pp. 759–774, Oct. 2018.
 M. Loushabi, M. Mazaheri, and J. Mohammd Vali Samani, “Inverse Solution of the advection-dispersion equation in rivers for pollution source identification”, Sharif J. Mech. Eng., vol. 35.3, no. 1, pp. 103–113, 2019. (In Persian)
 E. Permanoon and M. Mazaheri, “Identify the source of pollution with an Inverse-time analytical solution to the pollution transport equation,” Hydrophysics, vol. 6, no. 2, pp. 25–39, 2021. (In Persian)
 T. H. Skaggs and Z. J. Kabala, “Recovering the History of a Groundwater Contaminant Plume: Method of Quasi‐Reversibility,” Water Resour. Res., vol. 31, pp. 2669-2673, 1995.
 T. Zhang, H. Li, and S. Wang, “Identification of particulate contaminant source locations in enclosed spaces with inverse CFD modelling,” in 12th International Conference on Indoor Air Quality and Climate 2011, vol. 1, pp. 667–672, (2011).
 R. M. Neupauer, B. Borchers, and J. L. Wilson, “Comparison of inverse methods for reconstructing the release history of a groundwater contamination source,” Water Resour. Res., vol. 36, no. 9, pp. 2469–2475, 2000.
 C. S. Liu, “Group preserving scheme for backward heat conduction problems,” Int. J. Heat Mass Transf., vol. 47, no. 12–13, pp. 2567–2576, 2004.
 C. S. Liu, C. W. Chang, and J. R. Chang, “The backward group preserving scheme for 1D backward in time advection-dispersion equation,” Numer. Methods Partial Differ. Equ., vol. 26, no. 1, pp. 61–80, 2010.
 C. W. Chang and C. C. Kuo, “A Lie-group approach for solving backward two-dimensional nonlinear Klein-Gordon equation,” Procedia Eng., vol. 79, no. 1st ICM, pp. 590–598, 2014.
 S. Abbasbandy and M. S. Hashemi, “Group preserving scheme for the Cauchy problem of the Laplace equation,” Eng. Anal. Bound. Elem., vol. 35, no. 8, pp. 1003–1009, 2011.
 W. Gao, M. Partohaghighi, H. M. Baskonus, and S. Ghavi, “Regarding the group preserving scheme and method of line to the numerical simulations of Klein–Gordon model,” Results Phys., vol. 15, p. 102555, 2019.
 C. W. Chang and C. S. Liu, “The backward group preserving scheme for multi-dimensional nonhomogeneous and nonlinear backward wave problems,” Appl. Math. Model., vol. 38, no. 15–16, pp. 4027–4048, 2014.
 Y. Chen, “International Journal of Heat and Mass Transfer High order implicit and explicit Lie-group schemes for solving backward heat conduction problems,” Int. J. Heat Mass Transf., vol. 101, pp. 1016–1029, 2016.
 R. Noori, B. Ghiasi, H. Sheikhian, and J. F. Adamowski, “Estimation of the Dispersion Coefficient in Natural Rivers Using a Granular Computing Model,” J. Hydraul. Eng., vol. 143, no. 5, pp. 1–12, 2017.
 M. Ramezani, R. Noori, F. Hooshyaripor, Z. Deng, and A. Sarang, “Numerical modelling-based comparison of longitudinal dispersion coefficient formulas for solute transport in rivers,” Hydrol. Sci. J., vol. 64, no. 7, pp. 808–819, 2019.
 C. S. Liu, “Cone of non-linear dynamical system and group preserving schemes,” Int. J. Non. Linear. Mech., vol. 36, no. 7, pp. 1047–1068, 2001.
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