computational mathematics; numerically-asymptotical methods; theory of functions; mechanics of composite matherials; waves physics.
Main publications:
Bakhvalov N. S. Chislennye metody. M.: Nauka, 1973, 1975.
Bakhvalov N. S., Zhileikin Ya. M., Zabolotskaya E. A. Nelineinoe teoriya zvukovykh puchkov. M.: Nauka, 1982.
Bakhvalov N. S., Panasenko G. P. Osrednenie protsessov v periodicheskikh sredakh. Matematicheskie zadachi mekhaniki kompozitsionnykh materialov. M.: Nauka, 1984.
Bakhvalov N. S., Zhidkov N.P., Kobelkov G. M. Chislennye metody. M.: Nauka, 1987, 2000, 2001.
N. S. Bakhvalov, “Automatic construction of integration mesh for boundary value problems with boundary layers”, Zh. Vychisl. Mat. Mat. Fiz., 39:8 (1999), 1290–1295; Comput. Math. Math. Phys., 39:8 (1999), 1238–1243
N. S. Bakhvalov, K. Yu. Bogachev, Zh. F. Mètr, “An efficient algorithm for stiff elliptic problems with applications to the method of fictitious domains”, Zh. Vychisl. Mat. Mat. Fiz., 39:6 (1999), 919–931; Comput. Math. Math. Phys., 39:6 (1999), 884–896
N. S. Bakhvalov, M. È. Èglit, “Effective moduli of composites reinforced by systems of plates and bars”, Zh. Vychisl. Mat. Mat. Fiz., 38:5 (1998), 813–834; Comput. Math. Math. Phys., 38:5 (1998), 783–804
N. S. Bakhvalov, G. V. Sandrakov, M. È. Èglit, “Mathematical study of sound waves propagation progress in mixtures”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1996, no. 6, 19–21
N. S. Bakhvalov, G. P. Panasenko, M. È. Èglit, “The effective properties of structures and composites with inclusions in the form of walls and rods”, Zh. Vychisl. Mat. Mat. Fiz., 36:12 (1996), 73–79; Comput. Math. Math. Phys., 36:12 (1996), 1701–1706
N. S. Bakhvalov, M. È. Èglit, “Explicit computation of the effective characteristics of
composites that are reinforced by an unordered system of fibers”, Dokl. Akad. Nauk, 340:3 (1995), 295–299
N. S. Bakhvalov, M. È. Èglit, “The limiting behaviour of periodic media with soft-modular inclusions”, Zh. Vychisl. Mat. Mat. Fiz., 35:6 (1995), 905–917; Comput. Math. Math. Phys., 35:6 (1995), 719–729
N. S. Bakhvalov, M. È. Èglit, “Energy estimates in the case of nonapplicability of the Korn inequality, and orthogonal decompositions in spaces of matrices”, Trudy Mat. Inst. Steklov., 203 (1994), 21–32; Proc. Steklov Inst. Math., 203 (1995), 19–28
N. S. Bakhvalov, M. È. Èglit, “An estimate of the error of averaging the dynamics of small perturbations of very inhomogeneous mixtures”, Zh. Vychisl. Mat. Mat. Fiz., 34:3 (1994), 395–414; Comput. Math. Math. Phys., 34:3 (1994), 333–349
N. S. Bakhvalov, A. V. Knyazev, M. È. Èglit, “A Korn-type inequality and orthogonal decompositions in matrix
spaces”, Dokl. Akad. Nauk, 331:5 (1993), 536–537; Dokl. Math., 48:1 (1994), 127–129
N. S. Bakhvalov, M. È. Èglit, “Averaging of the equations of the dynamics of composites of slightly compressible elastic components”, Zh. Vychisl. Mat. Mat. Fiz., 33:7 (1993), 1066–1082; Comput. Math. Math. Phys., 33:7 (1993), 939–952
N. S. Bakhvalov, M. È. Èglit, “Propagation of small perturbations in weakly thermoconducting and
weakly viscous micrononhomogeneous media”, Dokl. Akad. Nauk, 325:1 (1992), 9–15; Dokl. Math., 46:1 (1993), 1–7
N. S. Bakhvalov, M. È. Èglit, “On the rate of propagation of perturbations in micro-inhomogeneous
elastic media with small shear elasticity”, Dokl. Akad. Nauk, 323:1 (1992), 13–18; Dokl. Math., 45:2 (1992), 239–244
N. S. Bakhvalov, A. V. Knyazev, “An effective iterative method for the solution of Lamé equations
for almost incompressible media and of Stokes equations”, Dokl. Akad. Nauk SSSR, 319:1 (1991), 13–17; Dokl. Math., 44:1 (1992), 4–9
N. S. Bakhvalov, A. V. Knyazev, “Effective computation of averaged characteristics of composites of
periodic structure that consist of essentially different materials”, Dokl. Akad. Nauk SSSR, 313:4 (1990), 777–781; Dokl. Math., 42:1 (1991), 57–62
N. S. Bakhvalov, A. V. Knyazev, “A new iterative algorithm for solving problems of the method of
fictitious flows for elliptic equations”, Dokl. Akad. Nauk SSSR, 312:4 (1990), 783–786; Dokl. Math., 41:3 (1990), 481–485
N. S. Bakhvalov, M. È. Èglit, “Variational properties of averaged equations for periodic media”, Trudy Mat. Inst. Steklov., 192 (1990), 5–19; Proc. Steklov Inst. Math., 192 (1992), 3–18
N. S. Bakhvalov, G. P. Panasenko, A. L. Štaras, “The averaging method for partial differential equations and its applications”, Itogi Nauki i Tekhniki. Ser. Sovrem. Probl. Mat. Fund. Napr., 34 (1988), 215–241
N. S. Bakhvalov, “Numerical solution of problems with nonsmooth data and interpolation theorems”, Trudy Mat. Inst. Steklov., 166 (1984), 18–22; Proc. Steklov Inst. Math., 166 (1986), 17–22
N. S. Bakhvalov, M. È. Èglit, “Processes in periodic media not describable in terms of mean characteristics”, Dokl. Akad. Nauk SSSR, 268:4 (1983), 836–840
1982
25.
N. S. Bakhvalov, M. Yu. Orekhov, “Fast methods for solving the Poisson equation”, Zh. Vychisl. Mat. Mat. Fiz., 22:6 (1982), 1386–1392; U.S.S.R. Comput. Math. Math. Phys., 22:6 (1982), 107–114
N. S. Bakhvalov, E. P. Zhidkov, E. P. Kadantseva, S. B. Rubin, S. I. Serdyukova, “Numerical modeling of the motion of a dense electron cloud in an inhomogeneous medium”, Zh. Vychisl. Mat. Mat. Fiz., 22:3 (1982), 685–689; U.S.S.R. Comput. Math. Math. Phys., 22:3 (1982), 193–198
N. S. Bakhvalov, B. I. Berezin, Þ. L. Bessonov, “Interpolation theorems for operators admitting estimates in terms of derivatives”, Dokl. Akad. Nauk SSSR, 256:6 (1981), 1296–1300
A. A. Amosov, N. S. Bakhvalov, J. I. Osipik, “Iteration processes for a problem of stationary heat exchange in a system of absolutely black bodies”, Zh. Vychisl. Mat. Mat. Fiz., 20:1 (1980), 104–111; U.S.S.R. Comput. Math. Math. Phys., 20:1 (1980), 110–120
N. S. Bakhvalov, S. I. Serdyukova, S. B. Rubin, E. P. Kadantseva, E. P. Zhidkov, “The numerical solution of a model selfconsistent electrodynamic problem”, Zh. Vychisl. Mat. Mat. Fiz., 19:5 (1979), 1228–1236; U.S.S.R. Comput. Math. Math. Phys., 19:5 (1979), 142–151
N. S. Bakhvalov, A. A. Zlotnik, “Coefficient stability of differential equations and averaging of equations with random coefficients”, Dokl. Akad. Nauk SSSR, 242:4 (1978), 745–748
N. S. Bakhvalov, V. S. Bondarenko, E. P. Zhidkov, S. B. Rubin, S. I. Serdyukova, “Numerical solution of maxwell's equations in an inhomogeneous region with a moving discontinuity on the right side”, Zh. Vychisl. Mat. Mat. Fiz., 16:3 (1976), 697–704; U.S.S.R. Comput. Math. Math. Phys., 16:3 (1976), 149–156
N. S. Bakhvalov, “Averaging of nonlinear partial differential equations with rapidly oscillating coefficients”, Dokl. Akad. Nauk SSSR, 225:2 (1975), 249–252
N. S. Bakhvalov, “A lower bound for the asymptotic characteristics of classes of functions with dominating mixed derivative”, Mat. Zametki, 12:6 (1972), 655–664; Math. Notes, 12:6 (1972), 833–838
N. S. Bakhvalov, “The optimization of methods of solution for ordinary differential equations with strongly oscillating solutions”, Zh. Vychisl. Mat. Mat. Fiz., 11:5 (1971), 1318–1322; U.S.S.R. Comput. Math. Math. Phys., 11:5 (1971), 287–292
N. S. Bakhvalov, “On the optimality of linear methods for operator approximation in convex classes of functions”, Zh. Vychisl. Mat. Mat. Fiz., 11:4 (1971), 1014–1018; U.S.S.R. Comput. Math. Math. Phys., 11:4 (1971), 244–249
N. S. Bakhvalov, M. Shtrekho, “Regularization of Ritz method on an example of polynomial approximation”, Mat. Zametki, 7:4 (1970), 483–493; Math. Notes, 7:4 (1970), 293–299
N. S. Bakhvalov, “The existence in the large of a regular solution of a quasilinear hyperbolic system”, Zh. Vychisl. Mat. Mat. Fiz., 10:4 (1970), 969–980; U.S.S.R. Comput. Math. Math. Phys., 10:4 (1970), 205–219
N. S. Bakhvalov, “The properties of optimal methods of solving problems in mathematical physics”, Zh. Vychisl. Mat. Mat. Fiz., 10:3 (1970), 555–568; U.S.S.R. Comput. Math. Math. Phys., 10:3 (1970), 1–19
N. S. Bakhvalov, “On the optimization of the methods for solving boundary value problems in the presence of a boundary layer”, Zh. Vychisl. Mat. Mat. Fiz., 9:4 (1969), 841–859; U.S.S.R. Comput. Math. Math. Phys., 9:4 (1969), 139–166
N. S. Bakhvalov, L. G. Vasil'eva, “Evaluation of the integrals of oscillating functions by interpolation at nodes of gaussian quadratures”, Zh. Vychisl. Mat. Mat. Fiz., 8:1 (1968), 175–181; U.S.S.R. Comput. Math. Math. Phys., 8:1 (1968), 241–249
N. S. Bakhvalov, “The asymptotics for small $\varepsilon$ of the solution of the equation $u_t+(\varphi(u))_{x}=\varepsilon u_{xx}$, corresponding to a rarefaction wave, in the degenerate case”, Zh. Vychisl. Mat. Mat. Fiz., 7:6 (1967), 1229–1236; U.S.S.R. Comput. Math. Math. Phys., 7:6 (1967), 25–36
N. S. Bakhvalov, “On the convergence of a relaxation method with natural constraints on the elliptic operator”, Zh. Vychisl. Mat. Mat. Fiz., 6:5 (1966), 861–883; U.S.S.R. Comput. Math. Math. Phys., 6:5 (1966), 101–135
N. S. Bakhvalov, “On the asymptotics with small $\varepsilon$ of the solution of the equation $u_t+(\varphi(u))_x=\varepsilon u_{xx}$, corresponding to a rarefaction wave”, Zh. Vychisl. Mat. Mat. Fiz., 6:3 (1966), 521–526; U.S.S.R. Comput. Math. Math. Phys., 6:3 (1966), 152–160
N. S. Bakhvalov, “Evaluations of the closeness of solutions of the Cauchy problem for non-linear differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 6:2 (1966), 229–237; U.S.S.R. Comput. Math. Math. Phys., 6:2 (1966), 47–58
N. S. Bakhvalov, “A lower bound for the randomness measure required in the use of the Monte Carlo method”, Zh. Vychisl. Mat. Mat. Fiz., 5:4 (1965), 760–763; U.S.S.R. Comput. Math. Math. Phys., 5:4 (1965), 252–257
N. S. Bakhvalov, “Optimal convergence bounds for quadrature processes and integration methods of Monte Carlo type for classes of functions”, Zh. Vychisl. Mat. Mat. Fiz., 4:supplement to № 4 (1964), 5–63
N. S. Bakhvalov, “On the hypothesis of the independence of round-off errors in numerical integration”, Zh. Vychisl. Mat. Mat. Fiz., 4:3 (1964), 399–404; U.S.S.R. Comput. Math. Math. Phys., 4:3 (1964), 1–8
N. S. Bakhvalov, “On optimal methods of specifying information during the solution of differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 2:4 (1962), 569–592; U.S.S.R. Comput. Math. Math. Phys., 2:4 (1963), 608–640
N. S. Bakhvalov, “Estimation of the error of numerical integration of a first-order quasilinear equation”, Zh. Vychisl. Mat. Mat. Fiz., 1:5 (1961), 771–783; U.S.S.R. Comput. Math. Math. Phys., 1:4 (1962), 926–938
N. S. Bakhvalov, “An estimate of the mean remainder term in quadrature formulae”, Zh. Vychisl. Mat. Mat. Fiz., 1:1 (1961), 64–77; U.S.S.R. Comput. Math. Math. Phys., 1:1 (1962), 68–82
N. S. Bakhvalov, “Construction of difference equations for an approximate solution of Laplace's equation”, Dokl. Akad. Nauk SSSR, 114:6 (1957), 1146–1148
N. S. Bakhvalov, “On the number of arithmetical operations in solving Poisson’s equation for a square by means of finite differences”, Dokl. Akad. Nauk SSSR, 113:2 (1957), 252–254
N. S. Bakhvalov, A. N. Bogolyubov, V. F. Butuzov, V. V. Voevodin, V. A. Il'in, A. S. Il'inskii, D. P. Kostomarov, E. I. Moiseev, A. A. Samarskii, “Aleksei Georgievich Sveshnikov (on his 80th birthday)”, Uspekhi Mat. Nauk, 60:2(362) (2005), 187–190; Russian Math. Surveys, 60:2 (2005), 389–393
N. S. Bakhvalov, A. N. Bogolyubov, V. F. Butuzov, V. V. Voevodin, V. A. Il'in, A. S. Il'inskii, D. P. Kostomarov, E. I. Moiseev, A. A. Samarskii, “Aleksei Georgievich Sveshnikov (on the occasion of his eightieth birthday)”, Zh. Vychisl. Mat. Mat. Fiz., 45:3 (2005), 371–373; Comput. Math. Math. Phys., 45:3 (2005), 353–355
2004
63.
N. S. Bakhvalov, V. S. Vladimirov, A. A. Gonchar, S. V. Emel'yanov, Yu. I. Zhuravlev, V. A. Il'in, V. V. Kozlov, S. K. Korovin, L. D. Kudryavtsev, O. B. Lupanov, V. P. Maslov, E. I. Moiseev, Yu. S. Osipov, D. E. Okhotsimskii, P. L. Ul'yanov, L. D. Faddeev, E. I. Shemyakin, “Viktor Antonovich Sadovnichii (A tribute in honor of his sixty-fifth birthday)”, Differ. Uravn., 40:4 (2004), 435–442; Differ. Equ., 40:4 (2004), 467–476
2001
64.
A. V. Arutyunov, N. S. Bakhvalov, M. E. Bogovskii, V. S. Vladimirov, A. A. Dezin, V. A. Il'in, E. F. Mishchenko, V. P. Maslov, S. M. Nikol'skii, S. V. Uspenskii, V. M. Filippov, “Vera Nikolaevna Maslennikova (obituary)”, Uspekhi Mat. Nauk, 56:4(340) (2001), 129–132; Russian Math. Surveys, 56:4 (2001), 739–743
N. S. Bakhvalov, M. I. Zelikin, A. S. Kalashnikov, V. L. Kamynin, O. A. Oleinik, E. Yu. Panov, N. S. Petrosyan, V. M. Tikhomirov, A. V. Faminskii, V. N. Chubarikov, “Stanislav Nikolaevich Kruzhkov (obituary)”, Uspekhi Mat. Nauk, 53:5(323) (1998), 213–220; Russian Math. Surveys, 53:5 (1998), 1071–1078
66.
N. S. Bakhvalov, O. V. Besov, S. M. Nikol'skii, M. K. Potapov, “Petr Lavrent'evich Ul'yanov (on his seventieth birthday)”, Uspekhi Mat. Nauk, 53:3(321) (1998), 211–220; Russian Math. Surveys, 53:3 (1998), 645–655
N. S. Bakhvalov, A. Yu. Belyaev, M. I. Vishik, V. V. Zhikov, V. P. Maslov, O. A. Oleinik, G. P. Panasenko, A. L. Piatnitski, “Sergei Mikhailovich Kozlov (obituary)”, Uspekhi Mat. Nauk, 51:4(310) (1996), 145–146; Russian Math. Surveys, 51:4 (1996), 723–725
N. S. Bakhvalov, S. P. Novikov, A. T. Fomenko, “Ol'ga Arsen'evna Oleinik (on her seventieth birthday)”, Uspekhi Mat. Nauk, 50:4(304) (1995), 177–186; Russian Math. Surveys, 50:4 (1995), 837–848
N. S. Bakhvalov, A. A. Il'yushin, A. Yu. Ishlinskii, O. B. Lupanov, V. A. Sadovnichii, A. T. Fomenko, “Olga Arsen'evna Oleynik”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1995, no. 5, 109–119
V. I. Arnol'd, N. S. Bakhvalov, K. V. Brushlinskii, I. M. Gel'fand, R. L. Dobrushin, A. V. Zabrodin, I. A. Ibragimov, S. P. Kurdyumov, S. P. Novikov, D. E. Okhotsimskii, Yu. V. Prokhorov, Yu. B. Radvogin, Ya. G. Sinai, R. Z. Khas'minskii, A. S. Holevo, A. N. Shiryaev, T. M. Eneev, “Nikolai Nikolaevich Chentsov (obituary)”, Uspekhi Mat. Nauk, 48:2(290) (1993), 165–168; Russian Math. Surveys, 48:2 (1993), 161–166
N. S. Bakhvalov, A. A. Borovkov, R. L. Dobrushin, A. V. Zabrodin, V. M. Zolotarev, I. A. Ibragimov, Yu. V. Prokhorov, B. A. Sevast'yanov, Ya. G. Sinai, A. V. Skorokhod, V. A. Statulyavichus, R. Z. Khas'minskii, A. S. Kholevo, D. M. Chibisov, A. N. Shiryaev, “Memorial: Nikolai Nikolaevitch Chentsov”, Teor. Veroyatnost. i Primenen., 38:3 (1993), 613–623; Theory Probab. Appl., 38:3 (1993), 506–515
N. S. Bakhvalov, V. S. Vladimirov, A. A. Gonchar, L. D. Kudryavtsev, V. I. Lebedev, S. M. Nikol'skii, S. P. Novikov, O. A. Oleinik, Yu. G. Reshetnyak, “Sergei L'vovich Sobolev (on his eightieth birthday)”, Uspekhi Mat. Nauk, 43:5(263) (1988), 3–16; Russian Math. Surveys, 43:5 (1988), 1–18
K. I. Babenko, N. S. Bakhvalov, V. M. Tikhomirov, V. B. Demidovich, “School-Seminar “Approximation Theory and Problems of Calculus Mathematics””, Uspekhi Mat. Nauk, 42:4(256) (1987), 221–222
1980
74.
A. N. Tikhonov, N. S. Bakhvalov, O. Yu. Tikhomirov, “Meeting-seminar of heads of departments of applied and computational mathematics of universities”, Izv. Vyssh. Uchebn. Zaved. Mat., 1980, no. 7, 86–88
P. S. Aleksandrov, R. A. Aleksandryan, V. M. Babich, N. S. Bakhvalov, O. V. Besov, L. V. Kantorovich, V. I. Lebedev, V. N. Maslennikova, O. A. Oleinik, S. V. Uspenskii, “Sergei L'vovich Sobolev (on his seventieth birthday)”, Uspekhi Mat. Nauk, 34:1(205) (1979), 3–15; Russian Math. Surveys, 34:1 (1979), 3–17
N. S. Bakhvalov, A. N. Tikhonov, “All-Union Conference on Computational Mathematics”, Uspekhi Mat. Nauk, 20:3(123) (1965), 254–255
77.
A. N. Tikhonov, N. S. Bakhvalov, “The all-union conference on computational mathematics”, Zh. Vychisl. Mat. Mat. Fiz., 5:4 (1965), 779–780; U.S.S.R. Comput. Math. Math. Phys., 5:4 (1965), 283–286
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