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Bakhvalov, Nikolai Sergeevich
(1934–2005)

Statistics Math-Net.Ru
Total publications: 65
Scientific articles: 49

Number of views:
This page:2298
Abstract pages:13167
Full texts:4966
References:456
Member of the Russian Academy of Sciences
Professor
Doctor of physico-mathematical sciences (1964)
Speciality: 01.01.07 (Computing mathematics)
Birth date: 29.05.1934
Keywords: 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.

http://www.mathnet.ru/eng/person11168
List of publications on Google Scholar
http://zbmath.org/authors/?q=ai:bakhvalov.nikolai-s
https://mathscinet.ams.org/mathscinet/MRAuthorID/29680

Publications in Math-Net.Ru
2006
1. N. S. Bakhvalov, M. È. Èglit, “High-order accurate equations describing vibrations of thin bars”, Zh. Vychisl. Mat. Mat. Fiz., 46:3 (2006),  457–472  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 46:3 (2006), 437–452  scopus
1999
2. N. S. Bakhvalov, “Efficient methods for stiff multidimensional multiparametric problems”, Zh. Vychisl. Mat. Mat. Fiz., 39:12 (1999),  2019–2049  mathnet  mathscinet  zmath  elib; Comput. Math. Math. Phys., 39:12 (1999), 1938–1966
3. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:8 (1999), 1238–1243
4. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 39:6 (1999), 884–896
1998
5. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:5 (1998), 783–804
1996
6. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:12 (1996), 1701–1706  isi
1995
7. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 35:6 (1995), 719–729  isi
1994
8. 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  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 203 (1995), 19–28
9. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 34:3 (1994), 333–349  isi
1993
10. 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  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 33:7 (1993), 939–952  isi
1990
11. N. S. Bakhvalov, M. È. Èglit, “Variational properties of averaged equations for periodic media”, Trudy Mat. Inst. Steklov., 192 (1990),  5–19  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 192 (1992), 3–18
1988
12. 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  mathnet  mathscinet  zmath
1984
13. N. S. Bakhvalov, “Numerical solution of problems with nonsmooth data and interpolation theorems”, Trudy Mat. Inst. Steklov., 166 (1984),  18–22  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 166 (1986), 17–22
1982
14. N. S. Bakhvalov, M. Yu. Orekhov, “Fast methods for solving the Poisson equation”, Zh. Vychisl. Mat. Mat. Fiz., 22:6 (1982),  1386–1392  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 22:6 (1982), 107–114
15. 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  mathnet  mathscinet; U.S.S.R. Comput. Math. Math. Phys., 22:3 (1982), 193–198
1981
16. N. S. Bakhvalov, B. I. Berezin, ř. L. Bessonov, “Interpolation theorems for operators admitting estimates in terms of derivatives”, Dokl. Akad. Nauk SSSR, 256:6 (1981),  1296–1300  mathnet  mathscinet  zmath
17. N. S. Bakhvalov, “Averaging of the heat transfer process in periodic media in the presence of radiation”, Differ. Uravn., 17:10 (1981),  1765–1773  mathnet  mathscinet
1980
18. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 20:1 (1980), 110–120
1979
19. N. S. Bakhvalov, “On the sound velocity in mixtures”, Dokl. Akad. Nauk SSSR, 245:6 (1979),  1345–1348  mathnet  mathscinet
20. 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  mathnet; U.S.S.R. Comput. Math. Math. Phys., 19:5 (1979), 142–151
1978
21. 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  mathnet  mathscinet  zmath
1976
22. 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  mathnet  zmath; U.S.S.R. Comput. Math. Math. Phys., 16:3 (1976), 149–156
1975
23. N. S. Bakhvalov, “Averaging of nonlinear partial differential equations with rapidly oscillating coefficients”, Dokl. Akad. Nauk SSSR, 225:2 (1975),  249–252  mathnet  mathscinet  zmath
24. N. S. Bakhvalov, “Averaging of partial differential equations with rapidly oscillating coefficients”, Dokl. Akad. Nauk SSSR, 221:3 (1975),  516–519  mathnet  mathscinet  zmath
1974
25. N. S. Bakhvalov, “Averaged characteristics of bodies with periodic structure”, Dokl. Akad. Nauk SSSR, 218:5 (1974),  1046–1048  mathnet  mathscinet
1972
26. 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  mathnet  mathscinet  zmath; Math. Notes, 12:6 (1972), 833–838
1971
27. N. S. Bakhvalov, “The stable calculation of polynomial values”, Zh. Vychisl. Mat. Mat. Fiz., 11:6 (1971),  1568–1574  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 11:6 (1971), 263–271
28. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 11:5 (1971), 287–292
29. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 11:4 (1971), 244–249
1970
30. N. S. Bakhvalov, M. Shtrekho, “Regularization of Ritz method on an example of polynomial approximation”, Mat. Zametki, 7:4 (1970),  483–493  mathnet  mathscinet  zmath; Math. Notes, 7:4 (1970), 293–299
31. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 10:4 (1970), 205–219
32. N. S. Bakhvalov, “The properties of optimal methods of solving problems in mathematical physics”, Zh. Vychisl. Mat. Mat. Fiz., 10:3 (1970),  555–568  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 10:3 (1970), 1–19
1969
33. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 9:4 (1969), 139–166
1968
34. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 8:1 (1968), 241–249
1967
35. N. S. Bakhvalov, “Parabolic systems with small parameters in the higher derivatives”, Dokl. Akad. Nauk SSSR, 174:2 (1967),  263–266  mathnet  mathscinet  zmath
36. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 7:6 (1967), 25–36
37. N. S. Bakhvalov, “On the optimal speed of integrating analytic functions”, Zh. Vychisl. Mat. Mat. Fiz., 7:5 (1967),  1011–1020  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 7:5 (1967), 63–75
1966
38. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 6:5 (1966), 101–135
39. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 6:3 (1966), 152–160
40. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 6:2 (1966), 47–58
1965
41. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 5:4 (1965), 252–257
1964
42. 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  mathnet  mathscinet  zmath
43. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 4:3 (1964), 1–8
1962
44. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 2:4 (1963), 608–640
1961
45. 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  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 1:4 (1962), 926–938
46. N. S. Bakhvalov, “An estimate of the mean remainder term in quadrature formulae”, Zh. Vychisl. Mat. Mat. Fiz., 1:1 (1961),  64–77  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 1:1 (1962), 68–82
1957
47. N. S. Bakhvalov, “Construction of difference equations for an approximate solution of Laplace's equation”, Dokl. Akad. Nauk SSSR, 114:6 (1957),  1146–1148  mathnet  mathscinet  zmath
48. N. S. Bakhvalov, “A method for an approximate solution of Laplace's equation”, Dokl. Akad. Nauk SSSR, 114:3 (1957),  455–458  mathnet  mathscinet  zmath
49. N. S. Bakhvalov, “On the number of arithmetical operations in solving Poissonís equation for a square by means of finite differences”, Dokl. Akad. Nauk SSSR, 113:2 (1957),  252–254  mathnet  mathscinet  zmath

2005
50. 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  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 60:2 (2005), 389–393  isi
51. 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  mathnet  mathscinet; Comput. Math. Math. Phys., 45:3 (2005), 353–355
2004
52. 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  mathnet  mathscinet; Differ. Equ., 40:4 (2004), 467–476
2001
53. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 56:4 (2001), 739–743  isi
1998
54. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:5 (1998), 1071–1078  isi
55. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 53:3 (1998), 645–655  isi
1996
56. 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  mathnet  mathscinet; Russian Math. Surveys, 51:4 (1996), 723–725  isi
1995
57. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 50:4 (1995), 837–848  isi
1993
58. 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  mathnet  mathscinet; Russian Math. Surveys, 48:2 (1993), 161–166  isi
59. 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  mathnet  mathscinet  zmath; Theory Probab. Appl., 38:3 (1993), 506–515  isi
1988
60. 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  mathnet  mathscinet  zmath; Russian Math. Surveys, 43:5 (1988), 1–18  isi
1987
61. 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  mathnet
1980
62. 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, 7,  86–88  mathnet
1979
63. 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  mathnet  mathscinet; Russian Math. Surveys, 34:1 (1979), 3–17
1965
64. N. S. Bakhvalov, A. N. Tikhonov, “All-Union Conference on Computational Mathematics”, Uspekhi Mat. Nauk, 20:3(123) (1965),  254–255  mathnet
65. A. N. Tikhonov, N. S. Bakhvalov, “The all-union conference on computational mathematics”, Zh. Vychisl. Mat. Mat. Fiz., 5:4 (1965),  779–780  mathnet; U.S.S.R. Comput. Math. Math. Phys., 5:4 (1965), 283–286

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