05.13.18 (Mathematical modelling, calculating methods, and the program systems)
E-mail:
Keywords:
Functional integral method, spin-fluctuation theory, dynamic general equilibrium models
Subject:
Variational methods in computational physics and economics
Main publications:
Melnikov, N., O'Neill, B.C., Dalton, M.G., “Accounting for household heterogeneity in general equilibrium economic growth models”, Energy Economics, 34:5 (2012), 1475–1483
Melnikov N. B., Reser B. I., Grebennikov V. I., “Extended dynamic spin-fluctuation theory of metallic magnetism”, J. Phys.: Condens. Matter, 23:27 (2011), 276003 (11 p.)
Melnikov N. B., Rezer B. I., “Optimalnoe gaussovo priblizhenie v teorii fluktuiruyuschego polya”, Trudy MIAN, 271 (2010), 159–180
Melnikov N. B., Reser B. I., Grebennikov V. I., “Spin-fluctuation theory beyond Gaussian approximation”, J. Phys. A: Math. Theor., 43 (2010), 195004 (19 p.)
Davydov A. A., Melnikov N. B., “Myagkaya poterya ustoichivosti v blochnoi modeli okeanicheskoi tsirkulyatsii s turbulentnymi potokami”, Trudy MIAN, 259 (2007), 10–19
N. B. Melnikov, B. I. Reser, “Asymptotic formulas for magnetization and chemical potential of ferromagnetic metals at low temperatures”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235 (2024), 78–86
2.
N. B. Melnikov, B. I. Reser, “Treatment of symmetry in the Ritz method for the Schrödinger equation in crystals with a basis”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 231 (2024), 74–82
3.
N. B. Melnikov, M. I. Ronzhina, “Chattering extremals in affine-in-contol stabilisation problems”, Uspekhi Mat. Nauk, 79:5(479) (2024), 187–188
2022
4.
B. M. Arystanbekov, N. B. Melnikov, “Projection Method for Infinite-Horizon Economic Growth Problems”, Trudy Inst. Mat. i Mekh. UrO RAN, 28:3 (2022), 17–29; Proc. Steklov Inst. Math. (Suppl.), 319, suppl. 1 (2022), S54–S65
2020
5.
N. B. Melnikov, G. V. Paradezhenko, B. I. Reser, “Numerical continuation method for nonlinear system of scalar and functional equations”, Zh. Vychisl. Mat. Mat. Fiz., 60:3 (2020), 405–412; Comput. Math. Math. Phys., 60:3 (2020), 404–410
N. B. Melnikov, G. V. Paradezhenko, B. I. Reser, “Effect of phonons on the magnetic characteristics of metals at finite temperatures”, TMF, 201:1 (2019), 137–148; Theoret. and Math. Phys., 201:1 (2019), 1531–1540
G. V. Paradezhenko, N. B. Melnikov, B. I. Reser, “Debye–Waller factor in neutron scattering by ferromagnetic metals”, TMF, 195:1 (2018), 91–104; Theoret. and Math. Phys., 195:1 (2018), 572–583
N. B. Melnikov, G. V. Paradezhenko, B. I. Reser, “Spin–density correlations and magnetic neutron scattering in ferromagnetic metals”, TMF, 191:1 (2017), 151–171; Theoret. and Math. Phys., 191:1 (2017), 602–619
Nikolai B. Melnikov, Arseniy P. Gruzdev, Michael G. Dalton, Brian C. O'Neill, “Parallel algorithm for calculating general equilibrium in multiregion economic growth models”, Ural Math. J., 2:2 (2016), 45–57
10.
G. V. Paradezhenko, N. B. Melnikov, B. I. Reser, “Spin-density correlator and its Fourier transform in the dynamic spin-fluctuation theory”, Num. Meth. Prog., 17:4 (2016), 474–486
N. B. Melnikov, G. V. Paradezhenko, “Magnetic phase transitions in spin-fluctuation theory”, TMF, 183:3 (2015), 486–497; Theoret. and Math. Phys., 183:3 (2015), 868–877
N. B. Melnikov, B. I. Reser, “Transverse susceptibility and the $T^{3/2}$ law in the dynamic spin-fluctuation theory”, TMF, 181:2 (2014), 358–373; Theoret. and Math. Phys., 181:2 (2014), 1435–1447
N. B. Melnikov, Yu. A. Romanenko, “Optimal Gaussian approximation in the Ising model”, Num. Meth. Prog., 13:3 (2012), 452–464
2011
15.
N. B. Melnikov, B. C. O'Neill, M. G. Dalton, “Accounting for household heterogeneity in dynamic general equilibrium models”, UBS, 35 (2011), 114–135
2010
16.
Nickolay B. Melnikov, Brian C. O'Neill, Michael G. Dalton, “Accounting for household heterogeneity in dynamic general equilibrium models”, Mat. Teor. Igr Pril., 2:4 (2010), 52–73
17.
N. B. Melnikov, B. C. O'Neill, M. G. Dalton, “Consumer aggregation in dynamic general equlibrium models with CES utility functions”, Trudy Inst. Mat. i Mekh. UrO RAN, 16:5 (2010), 289–296
18.
N. B. Melnikov, B. I. Reser, “Optimal Gaussian approximation in the fluctuating field theory”, Trudy Mat. Inst. Steklova, 271 (2010), 159–180; Proc. Steklov Inst. Math., 271 (2010), 149–170
N. B. Melnikov, “Непрерывная деформация модели экономического роста с перекрывающимися поколениями к модели Рамсея”, Matem. Mod. Kraev. Zadachi, 2 (2009), 107–110
2007
20.
A. A. Davydov, N. B. Melnikov, “Andronov–Hopf bifurcation in simple double diffusion models”, Uspekhi Mat. Nauk, 62:2(374) (2007), 175–176; Russian Math. Surveys, 62:2 (2007), 382–384
A. A. Davydov, N. B. Melnikov, “Soft Loss of Stability in an Ocean Circulation Box Model with Turbulent Fluxes”, Trudy Mat. Inst. Steklova, 259 (2007), 10–19; Proc. Steklov Inst. Math., 259 (2007), 6–15
N. B. Melnikov, “Optimality of Singular Curves in the Problem on a Car with $n$ Trailers”, CMFD, 19 (2006), 114–130; Journal of Mathematical Sciences, 151:6 (2008), 3543–3560
23.
M. I. Zelikin, N. B. Melnikov, “The Bellman function and optimal synthesis in control problems with nonsmooth constraints”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 110 (2006), 134–154; J. Math. Sci. (N. Y.), 121:2 (2004), 2281–2294
24.
N. B. Melnikov, “Extremal properties of singularities of Goursat distributions”, Uspekhi Mat. Nauk, 61:4(370) (2006), 191–192; Russian Math. Surveys, 61:4 (2006), 778–779
N. B. Melnikov, “A Saddle Point in a Differential Game on an Unbounded Time Interval”, Trudy Mat. Inst. Steklova, 236 (2002), 230–233; Proc. Steklov Inst. Math., 236 (2002), 218–221
2001
26.
M. I. Zelikin, N. B. Melnikov, R. Hildebrand, “The Topological Structure of the Phase Portrait of a Typical Fiber of Optimal Synthesis for Chattering Problems”, Trudy Mat. Inst. Steklova, 233 (2001), 125–152; Proc. Steklov Inst. Math., 233 (2001), 116–142
A. B. Kurzhanskii, N. B. Melnikov, “On the problem of control synthesis: the Pontryagin alternating integral and the Hamilton–Jacobi equation”, Mat. Sb., 191:6 (2000), 69–100; Sb. Math., 191:6 (2000), 849–881
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