boundary value problems; ordinary differential equations; eigenvalue problems; numerical methods.
Main publications:
Kurochkin S. V. Metod vyyavleniya neustoichivosti i poiska neustoichivykh sobstvennykh znachenii v zadache Orra–Zommerfelda // ZhVMiMF, 2001, 41 (1), 86–94.
Kurochkin S. V. O svoistvakh ustoichivosti metodov differentsialnoi progonki // ZhVMiMF, 2000, 40 (11), 1611–1614.
Kurochkin S. V. Chislennoe nakhozhdenie kraevogo usloviya vblizi osobennosti // ZhVMiMF, 1997, 37 (5), 543–552.
Kurochkin S. V. Metod nakhozhdeniya sobstvennykh znachenii nesamosopryazhennoi kraevoi zadachi // DAN, 1994, 336 (4), 442–443.
Kurochkin S. V. O singulyarnykh kraevykh zadachakh dlya lineinykh gamiltonovykh sistem // ZhVMiMF, 1994, 34 (1).
N. B. Konyukhova, S. V. Kurochkin, “Singular nonlinear problems for phase trajectories of some self-similar solutions of boundary layer equations: correct formulation, analysis, and calculations”, Zh. Vychisl. Mat. Mat. Fiz., 63:2 (2023), 245–261; Comput. Math. Math. Phys., 63:2 (2023), 202–217
2022
2.
T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin, “Optimal control of investment in a collective pension insurance model: study of singular nonlinear problems for integro-differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 62:9 (2022), 1473–1490; Comput. Math. Math. Phys., 62:9 (2022), 1438–1454
2021
3.
N. B. Konyukhova, S. V. Kurochkin, “Singular nonlinear problems for self-similar solutions of boundary-layer equations with zero pressure gradient: analysis and numerical solution”, Zh. Vychisl. Mat. Mat. Fiz., 61:10 (2021), 1619–1645; Comput. Math. Math. Phys., 61:10 (2021), 1603–1629
S. V. Kurochkin, “Neural network with smooth activation functions and without bottlenecks is almost surely a Morse function”, Zh. Vychisl. Mat. Mat. Fiz., 61:7 (2021), 1172–1178; Comput. Math. Math. Phys., 61:7 (2021), 1162–1168
2020
5.
S. V. Kurochkin, “Absence of bottlenecks in a neural network determines its generic functional properties”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 74–77; Dokl. Math., 101:1 (2020), 62–65
2019
6.
S. V. Kurochkin, “Detection of the homotopy type of an object using differential invariants of an approximating map”, Computer Optics, 43:4 (2019), 611–617
S. V. Kurochkin, “Existence conditions of negative eigenvalues in the regular Sturm–Liouville boundary value problem and explicit expressions for their number”, Zh. Vychisl. Mat. Mat. Fiz., 58:12 (2018), 2014–2025; Comput. Math. Math. Phys., 58:12 (2018), 1937–1947
T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin, “Dynamical insurance models with investment: Constrained singular problems for integrodifferential equations”, Zh. Vychisl. Mat. Mat. Fiz., 56:1 (2016), 47–98; Comput. Math. Math. Phys., 56:1 (2016), 43–92
A. A. Abramov, E. D. Kalinin, S. V. Kurochkin, “Calculation of the spheroidal functions of the first kind for complex values of the argument and parameters”, Zh. Vychisl. Mat. Mat. Fiz., 55:5 (2015), 798–806; Comput. Math. Math. Phys., 55:5 (2015), 788–796
T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin, “Singular initial-value and boundary-value problems for integrodifferential equations in dynamical insurance models with investments”, CMFD, 53 (2014), 5–29; Journal of Mathematical Sciences, 218:4 (2016), 369–394
S. V. Kurochkin, “Indexing of eigenvalues of boundary value problems for Hamiltonian systems of ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 54:3 (2014), 425–429; Comput. Math. Math. Phys., 54:3 (2014), 439–442
T. A. Belkina, N. B. Konyukhova, S. V. Kurochkin, “Singular boundary value problem for the integrodifferential equation in an insurance model with stochastic premiums: Analysis and numerical solution”, Zh. Vychisl. Mat. Mat. Fiz., 52:10 (2012), 1812–1846; Comput. Math. Math. Phys., 52:10 (2012), 1384–1416
A. A. Abramov, S. V. Kurochkin, “Calculation of solutions to the Mathieu equation and of related quantities”, Zh. Vychisl. Mat. Mat. Fiz., 47:3 (2007), 414–423; Comput. Math. Math. Phys., 47:3 (2007), 397–406
A. A. Abramov, S. V. Kurochkin, “Highly accurate calculation of radial spheroidal functions”, Zh. Vychisl. Mat. Mat. Fiz., 46:6 (2006), 996–1001; Comput. Math. Math. Phys., 46:6 (2006), 949–954
A. A. Abramov, S. V. Kurochkin, “Highly accurate calculation of agular spheroidal functions”, Zh. Vychisl. Mat. Mat. Fiz., 46:1 (2006), 12–17; Comput. Math. Math. Phys., 46:1 (2006), 10–15
A. L. Duischko, G. F. Zharkov, N. B. Konyukhova, S. V. Kurochkin, “Analytic–numerical investigation of the nonlinear boundary value problem for a superconducting plate in a magnetic field”, Zh. Vychisl. Mat. Mat. Fiz., 45:9 (2005), 1651–1676; Comput. Math. Math. Phys., 45:9 (2005), 1593–1617
V. A. Gani, N. B. Konyukhova, S. V. Kurochkin, V. A. Lenskii, “The investigation of charged topological soliton stability in the system of two interacting scalar fields”, Zh. Vychisl. Mat. Mat. Fiz., 44:11 (2004), 2069–2083; Comput. Math. Math. Phys., 44:11 (2004), 1968–1981
S. V. Kurochkin, “A method of detection of instability and for determination of unstable eigenvalues in the Orr–Sommerfeld problem”, Zh. Vychisl. Mat. Mat. Fiz., 41:1 (2001), 86–94; Comput. Math. Math. Phys., 41:1 (2001), 84–91
S. V. Kurochkin, “Numerical determination of a boundary condition near a singularity”, Zh. Vychisl. Mat. Mat. Fiz., 37:5 (1997), 543–552; Comput. Math. Math. Phys., 37:5 (1997), 529–538
S. V. Kurochkin, “Topological methods for the localization of eigenvalues of boundary value problems”, Zh. Vychisl. Mat. Mat. Fiz., 35:8 (1995), 1165–1174; Comput. Math. Math. Phys., 35:8 (1995), 933–939
S. V. Kurochkin, “A method for finding the eigenvalues of a nonselfadjoint boundary
value problem”, Dokl. Akad. Nauk, 336:4 (1994), 442–443; Dokl. Math., 49:3 (1994), 520–523
A. A. Abramov, N. B. Konyukhova, S. V. Kurochkin, B. S. Pariiskii, V. Yu. Prikhod'ko, “Numerical investigation of axisymmetric free oscillations in a vacuum and excitation in a compressible medium of a prolate cylindrical shell with hemispherical ends”, Zh. Vychisl. Mat. Mat. Fiz., 33:10 (1993), 1550–1580; Comput. Math. Math. Phys., 33:10 (1993), 1365–1390
S. V. Kurochkin, “The discrete character of the spectrum of a linear two-point boundary-value problem with constraints at singular points”, Zh. Vychisl. Mat. Mat. Fiz., 32:12 (1992), 1995–2000; Comput. Math. Math. Phys., 32:12 (1992), 1821–1826
S. V. Kurochkin, “Some estimates for the eigenvalues of a perturbation operator”, Zh. Vychisl. Mat. Mat. Fiz., 27:11 (1987), 1736–1739; U.S.S.R. Comput. Math. Math. Phys., 27:6 (1987), 88–90
1986
27.
S. V. Kurochkin, “Properties of Banach spaces related to projectivity”, Funktsional. Anal. i Prilozhen., 20:1 (1986), 75–76; Funct. Anal. Appl., 20:1 (1986), 64–66
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