01.01.07; 01.02.04 (Computing mathematics; Mechanics of deformable solids)
Birth date:
10.10.1950
E-mail:
Keywords:
the theory of the operators,
the discrete operators,
the traces of the operators,
the amendments of the theory of perturbations,
the hydrodynamical theory of stability.
Subject:
The new method of a calculation of the eigenvalues of the discrete operators is developed together with the academician of RAS V. A. Sadovnichii and professor V. V. Dubrovskii. The spectral problems of the hydrodynamical theory of stability of the current between two parallel planes (the problem of Оrra–Zomerfeld), the current between two rotating cylinders ( the movement of Cuatt) and the current in a round pipe (the movement of Puaziel) are solved using this method.
Biography
I have finished the physical faculty of the Rostov-na-Donu pedagogical institute in 1971. In 1985 I have protected the candidate dissertation. Has protected the thesis for a doctor's degree in 2004. Under my management have protected 4 post-graduate students master's theses. I have more than 90 publications.
Main publications:
Kravchenko V. F., Kadchenko S. I., Pustovoit V. I. Laminarnye, neizotermicheskie techeniya ferrozhidkosti v kanale pryamougolnogo secheniya // DAN. 1996. T. 347. # 2. S. 171–174.
Kadchenko S. I. Novyi metod vychisleniya sobstvennykh chisel spektralnoi zadachi Orra–Zommerfelda // Elektromagnitnye volny i elektronnye sistemy. 2000. T. 5. # 6. S. 4–10.
Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A. Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi gidrodinamicheskoi ustoichivosti techeniya Pauzeilya v krugloi trube // DAN. 2001. T. 380. # 2. S. 160–163.
Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A. Novyi metod vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi gidrodinamicheskoi ustoichivosti techeniya vyazkoi zhidkosti mezhdu dvumya vraschayuschimisya tsilindrami // DAN. 2001. T. 381. # 3. S. 320–324.
Dubrovskii V. V., Kadchenko S. I., Kravchenko V. F., Sadovnichii V. A. Novyi metod priblizhennogo vychisleniya pervykh sobstvennykh chisel spektralnoi zadachi Orra–Zommerfelda // DAN. 2001. T. 378. # 4. S. 443–446.
S. I. Kadchenko, A. V. Stavtceva, L. S. Ryazanova, V. V. Dubrovskii, “Algorithms for the computation of the eigenvalues of discrete semi-bounded operators defined on quantum graphs”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 15:1 (2023), 16–25
2.
S. I. Kadchenko, L. S. Ryazanova, “Algorithms invenire asymptotic formulas eigenvalues discreta semi-terminus operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 16:2 (2023), 104–110
2021
3.
S. I. Kadchenko, A. V. Stavtseva, L. S. Ryazanova, “Numerical methods for solving spectral problems on quantum graphs”, J. Comp. Eng. Math., 8:3 (2021), 49–70
4.
S. I. Kadchenko, L. S. Ryazanova, Yu. R. Dzhiganchina, “Algorithm for numerical solution of inverse spectral problems generated by Sturm–Liouville operators of an arbitrary even order”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 14:2 (2021), 52–63
2020
5.
S. I. Kadchenko, L. S. Ryazanova, I. E. Kadchenko, “Calculation of the eigenvalues of the problems generated by the arbitrary even order Sturm – Liouville operators”, J. Comp. Eng. Math., 7:3 (2020), 34–44
6.
S. I. Kadchenko, A. V. Pursheva, L. S. Ryazanova, “Solution of inverse spectral problems for discrete semi-bounded operators given on geometric graphs”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 13:4 (2020), 19–32
S. I. Kadchenko, G. A. Zakirova, L. S. Ryazanova, O. A. Torshina, “Calculation of discrete semi-bounded operators’ eigenvalues with large numbers”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 11:1 (2019), 10–15
2017
8.
S. I. Kadchenko, S. N. Kakushkin, “Calculation of spectral characteristics of perturbed self-adjoint operators by methods of regularized traces”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 141 (2017), 61–78; Journal of Mathematical Sciences, 241:5 (2019), 570–588
A. O. Kondyukov, T. G. Sukacheva, S. I. Kadchenko, L. S. Ryazanova, “Computational experiment for a class of mathematical models of magnetohydrodynamics”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:1 (2017), 149–155
S. I. Kadchenko, A. О. Kondyukov, “Numerical study of a flow of viscoelastic fluid of Kelvin–Voigt having zero order in a magnetic field”, J. Comp. Eng. Math., 3:2 (2016), 40–47
S. I. Kadchenko, O. A. Torshina, “Calculation of eigenvalues of elliptic differential operators using the theory of regularized series”, Vestn. Yuzhno-Ural. Gos. Un-ta. Ser. Matem. Mekh. Fiz., 8:2 (2016), 36–43
S. I. Kadchenko, S. N. Kakushkin, “Finding of values for sums of functional Rayleigh–Schrodinger series for perturbed self-adjoint operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:3 (2016), 137–143
15.
S. I. Kadchenko, E. A. Soldatova, S. A. Zagrebina, “Numerical research of the Barenblatt–Zheltov–Kochina stochastic model”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 9:2 (2016), 117–123
S. N. Kakushkin, S. I. Kadchenko, “The calculation of values of eigenfunctions of the perturbed self-adjoint operators by regularized traces method”, J. Comp. Eng. Math., 2:4 (2015), 48–60
S. I. Kadchenko, L. S. Ryazanova, A. I. Kadchenko, “Calculation of eigenvalues of Couette spectral problem by method of regularized traces”, J. Comp. Eng. Math., 2:4 (2015), 37–47
S. I. Kadchenko, “Numerical method for the solution of inverse problems generated by perturbations of self-adjoint operators by method of regularized traces”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2013, no. 6(107), 23–30
S. I. Kadchenko, “A Numerical Method for Solving Inverse Problems Generated by the Perturbed Self-Adjoint Operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 6:4 (2013), 15–25
S. I. Kadchenko, S. N. Kakushkin, “The calculating of meanings of eigen functions of discrete semibounded from below operators via method of regularized traces”, Vestnik Samarskogo Gosudarstvennogo Universiteta. Estestvenno-Nauchnaya Seriya, 2012, no. 6(97), 13–21
S. I. Kadchenko, S. N. Kakushkin, “The Algorithm of Finding of Meanings of Eigenfunctions of Perturbed Self-Adjoin Operators Via Method of Regularized Traces”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 14, 83–88
S. I. Kadchenko, S. N. Kakushkin, “The Numerical Methods of Eigenvalues and Eigenfunctions of Perturbed Self-Adjoin Operator Finding”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 13, 45–57
S. I. Kadchenko, S. N. Kakushkin, “Meanings of the First Eigenfunctions of Perturbed Discrete Operator with Simple Spectrum Finding”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2012, no. 11, 25–32
S. I. Kadchenko, S. N. Kakushkin, “The first four corrections of the perturbation theory for discrete semi bounded from below operators with free multiplicities of eigenvalues finding”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, no. 9, 16–21
27.
S. I. Kadchenko, L. S. Ryazanova, “Numeric method of finding the eigenvalues for the discrete lower semibounded operators”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 2011, no. 8, 46–51
S. I. Kadchenko, “Computing the sums of Rayleigh–Schrödinger series of perturbed self-adjoint operators”, Zh. Vychisl. Mat. Mat. Fiz., 47:9 (2007), 1494–1505; Comput. Math. Math. Phys., 47:9 (2007), 1435–1445
S. I. Kadchenko, I. I. Kinzina, “Computation of eigenvalues of perturbed discrete semibounded operators”, Zh. Vychisl. Mat. Mat. Fiz., 46:7 (2006), 1265–1272; Comput. Math. Math. Phys., 46:7 (2006), 1200–1206
S. I. Kadchenko, I. I. Kinzina, “Линейные уравнения для вычисления собственных чисел несамосопряженных операторов”, Matem. Mod. Kraev. Zadachi, 3 (2005), 117–120
2003
31.
S. I. Kadchenko, “Новый метод вычисления рядов поправок теории
возмущений дискретных операторов”, Vestnik Chelyabinsk. Gos. Univ., 2003, no. 9, 67–85
2000
32.
V. A. Sadovnichy, V. V. Dubrovskii, S. I. Kadchenko, V. F. Kravchenko, “Computation of the first eigenvalues of the hydrodynamic stability problem for a viscous fluid flow between two rotating cylinders”, Differ. Uravn., 36:6 (2000), 742–746; Differ. Equ., 36:6 (2000), 819–824
V. A. Sadovnichy, V. V. Dubrovskii, S. I. Kadchenko, V. F. Kravchenko, “Computation of the first eigenvalues of a boundary value problem on the hydrodynamic stability of a Poiseuille flow in a circular tube”, Differ. Uravn., 34:1 (1998), 50–53; Differ. Equ., 34:1 (1998), 49–53
V. F. Kravchenko, S. I. Kadchenko, V. I. Pustovoĭt, “Laminar nonisothermal flows of a ferrofluid in a channel of a rectangular cross-section”, Dokl. Akad. Nauk, 347:2 (1996), 171–174
2019
35.
A. D. Baev, Yu. E. Gliklikh, S. A. Zagrebina, A. A. Zamyshlyaeva, S. I. Kadchenko, A. V. Keller, D. V. Kostin, N. A. Manakova, V. I. Rjazhskih, G. A. Sviridyuk, T. G. Sukacheva, “Yu.I. Sapronov. To the memory of mathematician, teacher and friend”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 12:1 (2019), 166–168
2017
36.
A. A. Bayazitova, S. V. Brychev, E. V. Bychkov, V. V. Zagrebina, M. A. Zagrebin, S. A. Zagrebina, G. A. Zakirova, A. A. Zamyshlyaeva, S. I. Kadchenko, V. O. Kazak, A. V. Keller, O. G. Kitaeva, N. A. Manakova, P. O. Moskvicheva, A. B. Samarov, O. Tsyplenkova, D. E. Shafranov, M. M. Yakupov, “To the 65th anniversary of professor G. A. Sviridyuk”, Vestnik YuUrGU. Ser. Mat. Model. Progr., 10:2 (2017), 155–158
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