Belyaev, K. P.; Kuleshov, A. A.; Tuchkova, N. P. The stability problem for a dynamic system with the assimilation of observational data. (English) Zbl 1432.65097 Lobachevskii J. Math. 40, No. 7, 911-917 (2019). Summary: The problem of stability of a dynamic system defined by a system of differential equations to the perturbation of the initial data and with the data assimilation is considered. The assimilation of observational data is realized by the previously published author’s method. The stability condition for this data assimilation method is formulated in the classical sense of Lyapunov, and the solution of the system is corrected using observational data for a given time interval. Necessary and sufficient conditions are proposed under which this system is stable as a function of the observed values. A possible numerical experiment to test and to apply this theory is discussed. Cited in 3 Documents MSC: 65L07 Numerical investigation of stability of solutions to ordinary differential equations 37N30 Dynamical systems in numerical analysis Keywords:stability theory; stability conditions; data assimilation problem; generalized Kalman filter Software:HYCOM PDFBibTeX XMLCite \textit{K. P. Belyaev} et al., Lobachevskii J. Math. 40, No. 7, 911--917 (2019; Zbl 1432.65097) Full Text: DOI References: [1] M. Ghil and P. Malnotte-Rizzoli, “Data assimilation in meteorology and oceanography,” Adv. Geophys. 33, 141-266 1991. · doi:10.1016/S0065-2687(08)60442-2 [2] E. P. Chassignet, H. E. Hurlburt, E. J. Metzger, et al., “US GODAE: global ocean prediction with the HYbrid Coordinate Ocean Model (HYCOM),” Oceanography 22, 64-75 2009. · doi:10.5670/oceanog.2009.39 [3] L. N. Lima, L. P. Pezzi, S. G. Penny, and C. A. S. Tanajura, “An investigation of ocean model uncertainties through ensemble forecast experiments in the Southwest Atlantic Ocean,” J. Geophys. Res.: Oceans 124, 432-452 (2019). doi https://doi.org/10.1029/2018JC013919 · doi:10.1029/2018JC013919 [4] A. Schiller and G. B. Brassington, Operational Oceanography in the 21st Century (Springer Science, Heidelberg, 2011). doi https://doi.org/10.1007/978-94-007-0332-2_18 · doi:10.1007/978-94-007-0332-2 [5] M. Eslami, Theory of Sensitivity in Dynamic Systems, An Introduction (Springer, Heidelberg, 1994). · doi:10.1007/978-3-662-01632-9 [6] S. Breckling and M. Neda Fran Pahlevani, “A sensitivity study of the Navier-Stokes-<Emphasis Type=”Italic“>α model,” Comput. Math. Appl. 75, 666-689 2018. · Zbl 1409.76021 · doi:10.1016/j.camwa.2017.09.036 [7] E. Lorenz, “Deterministic nonperiodic flow,” J. Atmos. Sci. 20, 130-148 1963. · Zbl 1417.37129 · doi:10.1175/1520-0469(1963)020<0130:DNF>2.0.CO;2 [8] K. Belyaev, A. Kuleshov, N. Tuchkova, and C. A. S. Tanajura, “An optimal data assimilation method and its application to the numerical simulation of the ocean dynamics,” Math. Comput. Model. Dyn. Syst. 24, 12-25 (2018). doi https://doi.org/10.1080/13873954.2017.1338300 · Zbl 1484.86018 · doi:10.1080/13873954.2017.1338300 [9] K. Belyaev, A. Kuleshov, N. Tuchkova, and C. A. S. Tanajura, “A correction method for dynamic model calculations using observational data and its application in oceanography,” Math. Models Comput. Simul. 8, 391-400 (2016). doi https://doi.org/10.1134/S2070048216040049 · doi:10.1134/S2070048216040049 [10] K. Belyaev, N. Tuchkova, and C. A. S. Tanajura, “Comparison of methods for argo drifters data assimilation into a hydrodynamical model of the ocean,” Oceanology 52, 593-603 (2012). doi https://doi.org/10.1134/S0001437012050025 · doi:10.1134/S0001437012050025 [11] I. Gikhman and A. Skorokhod, Introduction to the Theory of Random Processes (Dover, New York, 1996). · Zbl 0573.60003 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.