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Publications in Math-Net.Ru |
Citations |
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2022 |
1. |
A. I. Tolstykh, D. A. Shirobokov, “On Tollmien – Schlichting instability in numerical solutions of the Navier – Stokes equations obtained with 16th-order multioperators-based scheme”, Computer Research and Modeling, 14:4 (2022), 953–967 |
2. |
M. V. Lipavskii, A. I. Tolstykh, D. A. Shirobokov, “Parallel implementation of the 16th-order multioperator scheme: application to problems of instability of vortices and boundary layers”, Matem. Mod., 34:8 (2022), 3–18 ; Math. Models Comput. Simul., 15:2 (2023), 167–176 |
3. |
A. I. Tolstykh, D. A. Shirobokov, “Excitation and development of instability in a compressible boundary layer as obtained in high-order accurate numerical simulation without introducing artificial perturbations”, Zh. Vychisl. Mat. Mat. Fiz., 62:7 (2022), 1209–1223 ; Comput. Math. Math. Phys., 62:7 (2022), 1180–1192 |
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2018 |
4. |
A. I. Tolstykh, E. N. Chigerev, “Application of compact and multioperator approximations in the immersed boundary method”, Zh. Vychisl. Mat. Mat. Fiz., 58:8 (2018), 157–181 ; Comput. Math. Math. Phys., 58:8 (2018), 1354–1376 |
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2016 |
5. |
A. I. Tolstykh, “On the use of multioperators in the construction of high-order grid approximations”, Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016), 943–957 ; Comput. Math. Math. Phys., 56:6 (2016), 932–946 |
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2013 |
6. |
A. I. Tolstykh, “Hybrid schemes with high-order multioperators for computing discontinuous solutions”, Zh. Vychisl. Mat. Mat. Fiz., 53:9 (2013), 1481–1502 ; Comput. Math. Math. Phys., 53:9 (2013), 1303–1322 |
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7. |
M. V. Lipavskii, A. I. Tolstykh, “Tenth-order accurate multioperator scheme and its application in direct numerical simulation”, Zh. Vychisl. Mat. Mat. Fiz., 53:4 (2013), 600–614 ; Comput. Math. Math. Phys., 53:4 (2013), 455–468 |
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8. |
M. V. Lipavskii, A. I. Tolstykh, E. N. Chigerev, “Numerical simulation of shear layer instability using a scheme with ninth-order multioperator approximations”, Zh. Vychisl. Mat. Mat. Fiz., 53:3 (2013), 417–432 ; Comput. Math. Math. Phys., 53:3 (2013), 296–310 |
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2011 |
9. |
A. I. Tolstykh, “Family of fifth-order three-level schemes for evolution problems”, Zh. Vychisl. Mat. Mat. Fiz., 51:2 (2011), 206–221 ; Comput. Math. Math. Phys., 51:2 (2011), 193–207 |
10. |
A. I. Tolstykh, “On the multioperator method for constructing approximations and finite difference schemes of an arbitrarily high order”, Zh. Vychisl. Mat. Mat. Fiz., 51:1 (2011), 56–73 ; Comput. Math. Math. Phys., 51:1 (2011), 51–67 |
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2010 |
11. |
A. I. Tolstykh, “On families of compact fourth- and fifth-order approximations involving the inversion of two-point operators for equations with convective terms”, Zh. Vychisl. Mat. Mat. Fiz., 50:5 (2010), 894–907 ; Comput. Math. Math. Phys., 50:5 (2010), 848–861 |
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2009 |
12. |
A. D. Savel'ev, A. I. Tolstykh, D. A. Shirobokov, “Application of compact and multioperator schemes to the numerical simulation of acoustic fields generated by instability waves in supersonic jets”, Zh. Vychisl. Mat. Mat. Fiz., 49:7 (2009), 1280–1294 ; Comput. Math. Math. Phys., 49:7 (2009), 1221–1234 |
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2006 |
13. |
M. V. Lipavskii, A. I. Tolstykh, E. N. Chigerëv, “A parallel computational scheme with ninth-order multioperator approximations and its application to direct numerical simulation”, Zh. Vychisl. Mat. Mat. Fiz., 46:8 (2006), 1433–1452 ; Comput. Math. Math. Phys., 46:8 (2006), 1359–1377 |
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2005 |
14. |
A. I. Tolstykh, D. A. Shirobokov, “Meshless method based on radial basis functions”, Zh. Vychisl. Mat. Mat. Fiz., 45:8 (2005), 1498–1505 ; Comput. Math. Math. Phys., 45:8 (2005), 1447–1454 |
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2003 |
15. |
M. V. Lipavskii, A. I. Tolstykh, “Fifth- and seventh-order accurate multioperator schemes”, Zh. Vychisl. Mat. Mat. Fiz., 43:7 (2003), 1018–1034 ; Comput. Math. Math. Phys., 43:7 (2003), 975–990 |
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2002 |
16. |
A. I. Tolstykh, “Integro-interpolation schemes of a given order and other applications of the multioperator principle”, Zh. Vychisl. Mat. Mat. Fiz., 42:11 (2002), 1712–1726 ; Comput. Math. Math. Phys., 42:11 (2002), 1647–1660 |
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2000 |
17. |
A. I. Tolstykh, “Construction of schemes of prescribed order of accuracy with linear combinations of operators”, Zh. Vychisl. Mat. Mat. Fiz., 40:8 (2000), 1206–1220 ; Comput. Math. Math. Phys., 40:8 (2000), 1159–1172 |
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1999 |
18. |
M. V. Lipavskii, A. I. Tolstykh, “Comparative efficiency of schemes based on upwind compact approximations”, Zh. Vychisl. Mat. Mat. Fiz., 39:10 (1999), 1705–1720 ; Comput. Math. Math. Phys., 39:10 (1999), 1636–1650 |
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1997 |
19. |
V. N. Koterov, A. D. Savel'ev, A. I. Tolstykh, “Numerical simulation of aero-optical fields near an open port of airborne observatory”, Matem. Mod., 9:1 (1997), 27–39 |
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1996 |
20. |
A. I. Tolstykh, D. A. Shirobokov, “Difference schemes with fifth-order compact approximations for three-dimensional viscous gas flows”, Zh. Vychisl. Mat. Mat. Fiz., 36:4 (1996), 71–85 ; Comput. Math. Math. Phys., 36:4 (1996), 477–489 |
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1992 |
21. |
A. I. Tolstykh, “Iterative schemes with noncentered compact approximations”, Dokl. Akad. Nauk, 326:3 (1992), 425–430 ; Dokl. Math., 46:2 (1993), 290–295 |
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1991 |
22. |
A. I. Tolstykh, “A class of noncentered fifth-order compact difference schemes
based on Padé approximations”, Dokl. Akad. Nauk SSSR, 319:1 (1991), 72–77 ; Dokl. Math., 44:1 (1992), 69–74 |
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1990 |
23. |
V. A. Garanzha, A. I. Tolstykh, “Numerical modeling of unsteady separated flows of incompressible liquid based on the fifth-order compact approximations”, Dokl. Akad. Nauk SSSR, 312:2 (1990), 311–314 |
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1989 |
24. |
A. I. Tolstykh, “Compact third-order approximations in algorithms for an incompressible fluid”, Zh. Vychisl. Mat. Mat. Fiz., 29:10 (1989), 1514–1529 ; U.S.S.R. Comput. Math. Math. Phys., 29:5 (1989), 183–195 |
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1988 |
25. |
A. P. Byrkin, A. I. Tolstykh, “Compact third- and fourth-order schemes in problems concerning internal flows of viscous and non-viscous gases”, Zh. Vychisl. Mat. Mat. Fiz., 28:8 (1988), 1234–1251 ; U.S.S.R. Comput. Math. Math. Phys., 28:4 (1988), 180–191 |
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1987 |
26. |
A. D. Savel'ev, A. I. Tolstykh, “Algorithms for calculating viscous gas flows based on compact third-order approximations”, Zh. Vychisl. Mat. Mat. Fiz., 27:11 (1987), 1709–1724 ; U.S.S.R. Comput. Math. Math. Phys., 27:6 (1987), 71–80 |
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1986 |
27. |
A. I. Tolstykh, “A third-order scheme and some of its applications”, Dokl. Akad. Nauk SSSR, 291:1 (1986), 45–49 |
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1985 |
28. |
A. I. Tolstykh, “Nonsymmetric three-point difference schemes of the fourth and fifth order”, Zh. Vychisl. Mat. Mat. Fiz., 25:8 (1985), 1164–1175 ; U.S.S.R. Comput. Math. Math. Phys., 25:4 (1985), 127–134 |
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1984 |
29. |
M. V. Lipavskii, A. I. Tolstykh, “The small parameter method for the numerical study of the flow of a stratified medium”, Zh. Vychisl. Mat. Mat. Fiz., 24:5 (1984), 771–775 ; U.S.S.R. Comput. Math. Math. Phys., 24:3 (1984), 95–97 |
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1983 |
30. |
A. I. Tolstykh, “An internal iteration method for solving three-dimensional
problems with nonselfadjoint operators”, Dokl. Akad. Nauk SSSR, 272:3 (1983), 538–541 |
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1982 |
31. |
O. M. Belotserkovskii, A. P. Byrkin, A. P. Mazurov, A. I. Tolstykh, “A difference method of increased accuracy for the calculation of flows of a viscous gas”, Zh. Vychisl. Mat. Mat. Fiz., 22:6 (1982), 1480–1490 ; U.S.S.R. Comput. Math. Math. Phys., 22:6 (1982), 206–216 |
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1981 |
32. |
A. I. Tolstykh, “Implicit schemes of higher accuracy for systems of equations”, Zh. Vychisl. Mat. Mat. Fiz., 21:2 (1981), 339–354 ; U.S.S.R. Comput. Math. Math. Phys., 21:2 (1981), 83–98 |
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1978 |
33. |
A. I. Tolstykh, “Condensation of the nodes of the difference networks in the solution process, and the application of schemes of improved accuracy in the numerical study of viscous gas flows”, Zh. Vychisl. Mat. Mat. Fiz., 18:1 (1978), 139–153 ; U.S.S.R. Comput. Math. Math. Phys., 18:1 (1978), 134–147 |
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1976 |
34. |
A. I. Tolstykh, “Implicit difference schemes of third order accuracy for multidimensional problems”, Zh. Vychisl. Mat. Mat. Fiz., 16:5 (1976), 1182–1190 ; U.S.S.R. Comput. Math. Math. Phys., 16:5 (1976), 92–100 |
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1975 |
35. |
A. N. Minailos, A. I. Tolstykh, “Implicit high-accuracy finite-difference schemes for the “shock capturing” calculation of discontinuous”, Zh. Vychisl. Mat. Mat. Fiz., 15:2 (1975), 527–531 ; U.S.S.R. Comput. Math. Math. Phys., 15:2 (1975), 242–247 |
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1973 |
36. |
A. I. Tolstykh, “On the method of numerical solution of Navier–Stokes equations for a compressible gas in wide range of Reynolds numbers”, Dokl. Akad. Nauk SSSR, 210:1 (1973), 48–51 |
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1970 |
37. |
O. M. Belotserkovskii, F. D. Popov, A. I. Tolstykh, V. N. Fomin, A. S. Kholodov, “Numerical solution of certain problems in gas dynamics”, Zh. Vychisl. Mat. Mat. Fiz., 10:2 (1970), 401–416 ; U.S.S.R. Comput. Math. Math. Phys., 10:2 (1970), 158–177 |
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1966 |
38. |
A. I. Tolstykh, “Numerical computation of the supersonic flow of a viscous gas round a blunt body”, Zh. Vychisl. Mat. Mat. Fiz., 6:1 (1966), 113–120 ; U.S.S.R. Comput. Math. Math. Phys., 6:1 (1966), 160–170 |
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2017 |
39. |
I. B. Petrov, B. N. Chetverushkin, Vl. V. Voevodin, V. A. Gushchin, K. V. Rudakov, A. I. Tolstykh, A. A. Shananin, A. I. Lobanov, G. Yu. Riznichenko, A. V. Borisov, A. V. Koganov, V. I. Kosarev, S. A. Ishanov, I. S. Nikitin, V. B. Pirogov, A. A. Polezhaev, G. A. Tirskii, I. G. Tormasov, S. S. Simakov, E. L. Stupitsky, P. S. Utkin, Ya. A. Kholodov, V. L. Yakushev, “In memory of A. S. Kholodov”, Computer Research and Modeling, 9:5 (2017), 677–678 |
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2016 |
40. |
B. N. Chetverushkin, V. B. Betelin, A. S. Kholodov, V. A. Gushchin, S. L. Chernyshev, I. B. Petrov, A. I. Tolstykh, L. I. Turchak, A. V. Babakov, V. L. Yakushev, O. V. Troshkin, “In memory of O. M. Belotserkovskii”, Matem. Mod., 28:2 (2016), 3–5 |
41. |
A. V. Babakov, V. B. Betelin, V. A. Gushchin, N. S. Vishnyakov, M. K. Kerimov, I. B. Petrov, A. I. Tolstykh, O. V. Troshkin, L. I. Turchak, A. S. Kholodov, S. L. Chernyshov, B. N. Chetverushkin, V. L. Yakushev, “In memory of Academician of the RAS Oleg Mikhailovich Belotserkovskii”, Zh. Vychisl. Mat. Mat. Fiz., 56:6 (2016), 921–926 ; Comput. Math. Math. Phys., 56:6 (2016), 911–915 |
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