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Kulikov, Gennady Yur'evich

Statistics Math-Net.Ru
Total publications: 25
Scientific articles: 25

Number of views:
This page:2270
Abstract pages:6654
Full texts:2210
References:688
Associate professor
Doctor of physico-mathematical sciences (2002)
Speciality: 05.13.18; 05.13.17 (Mathematical modeling, numerical methods, and the program systems; Theoretical foundation for informatics)
Birth date: 27.10.1965
E-mail:
Website: http://fenix.tecnico.ulisboa.pt/homepage/ist25063
Keywords: Numerical methods; initial value problem for ordinary differential equations; differential-algebraic systems, global error estimation and control techniques; extended, unscented and cubature Kalman filters.
UDC: 519.622, 519.61, 519.622.2, 519.622.1
MSC: 34B16, 65C60, 65L05, 65L06, 65L20, 65L50, 65L70, 65L80, 93E11

Subject:

Numerical methods for ordinary differential equations and differential-algebraic systems; global error estimation and control techniques; applications in fluid mechanics; nonlinear Kalman filtering algorithms.

Biography

2014–date Senior Research Fellow (FCT Investigador 2013), CEMAT (Centro de Matemática e Aplicações), Instituto Superior Técnico, Universidade de Lisboa, Portugal
2009–2013 Research Associate (Ciência 2008), CEMAT (Centro de Matemática e Aplicações), Instituto Superior Técnico, Universidade Técnica de Lisboa, Portugal
2007–2009 Reader, School of Computational and Applied Mathematics, Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa
2004–2007 Senior Lecturer, School of Computational and Applied Mathematics, Faculty of Science, University of the Witwatersrand, Johannesburg, South Africa
2001–2003 Associate Professor, Faculty of Mechanics and Mathematics, Ulyanovsk State University, Ulyanovsk, Russian Federation
1998–2001 Senior Research Fellow, Associate Professor and Head of Laboratory for Mathematical Modelling, Faculty of Mechanics and Mathematics, Ulyanovsk State University, Ulyanovsk, Russian Federation
1996–1998 Associate Professor and Head of Laboratory for Mathematical Modelling, Faculty of Mechanics and Mathematics, Ulyanovsk State University, Ulyanovsk, Russian Federation
1995–1996 Senior Lecturer and Head of Laboratory for Mathematical Modelling, Faculty of Mechanics and Mathematics, Ulyanovsk branch of Moscow State University, Russian Federation
1993–1995 Assistant Professor, Faculty of Mechanics and Mathematics, Ulyanovsk branch of Moscow State University, Ulyanovsk, Russian Federation

   
Main publications:
  1. G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems”, Comput. Math. Math. Phys., 55:6 (2015), 983–1003  mathnet  crossref  crossref  mathscinet  isi  elib  elib  elib  elib  scopus  scopus
  2. G. Yu. Kulikov, M. V. Kulikova, “High-order accurate continuous-discrete extended Kalman filter for chemical engineering”, European Journal of Control, 2015, no. 21, 14–26  crossref  mathscinet  zmath  isi  scopus
  3. G. Yu. Kulikov, R. Weiner, “A singly diagonally implicit two-step peer triple with global error control for stiff ordinary differential equations”, SIAM Journal on Scientific Computing, 37:3 (2015), A1593–A1613  crossref  mathscinet  zmath  isi  scopus
  4. G. Yu. Kulikov, M. V. Kulikova, “The accurate continuous-discrete extended Kalman filter for continuous-time stochastic systems”, Russian Journal of Numerical Analysis and Mathematical Modelling, 30:4 (2015), 239–249  crossref  mathscinet  zmath  isi  scopus
  5. G. Yu. Kulikov, M. V. Kulikova, “Accurate numerical implementation of the continuous-discrete extended Kalman filter”, IEEE Transactions on Automatic Control, 59:1 (2014), 273–279  crossref  mathscinet  zmath  isi  scopus
  6. R. Weiner, G. Yu. Kulikov, “Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods”, Comput. Math. Math. Phys., 54:4 (2014), 604–619  mathnet  crossref  crossref  mathscinet  isi  elib  elib  elib  elib  scopus  scopus
  7. G. Yu. Kulikov, P. M. Lima, M. L. Morgado, “Analysis and numerical approximation of singular boundary value problems with the p-Laplacian in fluid mechanics”, Journal of Computational and Applied Mathematics, 262 (2014), 87-104  crossref  mathscinet  zmath  isi  scopus
  8. R. Weiner, G. Yu. Kulikov, “Local and global error estimation and control within explicit two-step peer triples”, Journal of Computational and Applied Mathematics, 262 (2014), 261-270  crossref  mathscinet  zmath  isi  scopus
  9. G. Yu. Kulikov, “Cheap global error estimation in some Runge-Kutta pairs”, IMA Journal of Numerical Analysis, 33:1 (2013), 136-163  crossref  mathscinet  zmath  isi  scopus
  10. G.Yu. Kulikov, “Global error control in adaptive Nordsieck methods”, SIAM Journal on Scientific Computing, 34:2 (2012), A839-A860  crossref  mathscinet  zmath  isi  scopus
  11. R. Weiner, G.Yu. Kulikov, H. Podhaisky, “Variable-stepsize doubly quasi-consistent parallel explicit peer methods with global error control”, Applied Numerical Mathematics, 62:10 (2012), 1591-1603  crossref  mathscinet  zmath  isi  scopus
  12. G. Yu. Kulikov, “Solving the order reduction phenomenon in variable step size quasi-consistent Nordsieck methods”, Comput. Math. Math. Phys., 52:11 (2012), 1547–1564  mathnet  crossref  mathscinet  isi  elib  elib  elib  elib  scopus  scopus
  13. G.Yu. Kulikov, R. Weiner, “Global error estimation and control in linearly-implicit parallel two-step peer W-methods”, Journal of Computational and Applied Mathematics, 236:6 (2011), 1226–1239  crossref  mathscinet  zmath  isi  scopus
  14. G.Yu. Kulikov, “Proportional extrapolation and symmetric one-step methods”, Russian Journal of Numerical Analysis and Mathematical Modelling, 26:1 (2011), 49-73  crossref  mathscinet  zmath  isi  scopus
  15. G.Yu. Kulikov, R. Weiner, “Variable-stepsize interpolating explicit parallel peer methods with inherent global error control”, SIAM Journal on Scientific Computing, 32:4 (2010), 1695-1723  crossref  mathscinet  zmath  isi  scopus
  16. G.Yu. Kulikov, R. Weiner, “Doubly quasi-consistent parallel explicit peer methods with built-in global error estimation”, Journal of Computational and Applied Mathematics, 233:9 (2010), 2351-2364  crossref  mathscinet  zmath  adsnasa  isi  scopus
  17. G.Yu. Kulikov, “Local theory of extrapolation methods”, Numerical Algorithms, 53 (2010), 321-342  crossref  mathscinet  zmath  isi  elib  scopus
  18. G.Yu. Kulikov, “On quasi-consistent integration by Nordsieck methods”, Journal of Computational and Applied Mathematics, 225:1 (2009), 268-287  crossref  mathscinet  zmath  adsnasa  isi  scopus
  19. G.Yu. Kulikov, S.K. Shindin, “Adaptive nested implicit Runge-Kutta formulas of Gauss type”, Applied Numerical Mathematics, 59:3-4 (2009), 707-722  crossref  mathscinet  zmath  isi  elib  scopus
  20. G.Yu. Kulikov, S.K. Shindin, “Local and global error estimation in Nordsieck methods”, Russian Journal of Numerical Analysis and Mathematical Modelling, 23:6 (2008), 567-595  crossref  mathscinet  zmath  isi  scopus
  21. G.Yu. Kulikov, S.K. Shindin, “Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems”, BIT Numerical Mathematics, 45 (2005), 517-542  crossref  mathscinet  zmath  isi  elib  scopus
  22. G. Yu. Kulikov, A. A. Korneva, G. Ya. Benderskaya, “On numerical solution of large-scale systems of index 1 differential-algebraic equations”, Fundam. Prikl. Mat., 7:4 (2001), 1047–1080  mathnet  mathscinet  zmath

http://www.mathnet.ru/eng/person19468
http://scholar.google.com/citations?user=JLHwbPcAAAAJ&hl=en
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/335687
http://orcid.org/0000-0002-1663-6009
http://www.researcherid.com/rid/J-1669-2012
http://www.scopus.com/authid/detail.url?authorId=7102426626

Publications in Math-Net.Ru
2015
1. G. Yu. Kulikov, “Embedded symmetric nested implicit Runge–Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems”, Zh. Vychisl. Mat. Mat. Fiz., 55:6 (2015),  986–1007  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 55:6 (2015), 983–1003  isi  elib  scopus
2014
2. R. Weiner, G. Yu. Kulikov, “Efficient error control in numerical integration of ordinary differential equations and optimal interpolating variable-stepsize peer methods”, Zh. Vychisl. Mat. Mat. Fiz., 54:4 (2014),  591–607  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 54:4 (2014), 604–619  isi  elib  scopus
2012
3. G. Yu. Kulikov, “Solving the order reduction phenomenon in variable step size quasi-consistent Nordsieck methods”, Zh. Vychisl. Mat. Mat. Fiz., 52:11 (2012),  2004–2022  mathnet  mathscinet  elib; Comput. Math. Math. Phys., 52:11 (2012), 1547–1564  isi  elib  scopus
2011
4. G. Yu. Kulikov, E. B. Kuznetsov, E. Yu. Khrustaleva, “On the global error control in nested implicit Runge–Kutta methods of Gauss type”, Sib. Zh. Vychisl. Mat., 14:3 (2011),  245–259  mathnet; Num. Anal. Appl., 4:3 (2011), 199–209  scopus
2010
5. G. Yu. Kulikov, E. Yu. Khrustalëva, “On the automatic control of step size and order in one-step collocation methods with higher derivatives”, Zh. Vychisl. Mat. Mat. Fiz., 50:6 (2010),  1060–1077  mathnet  mathscinet; Comput. Math. Math. Phys., 50:6 (2010), 1006–1023  isi  scopus
2008
6. G. Yu. Kulikov, E. Y. Khrustaleva, “Automatic step size and order control in implicit one-step extrapolation methods”, Zh. Vychisl. Mat. Mat. Fiz., 48:9 (2008),  1580–1606  mathnet  mathscinet; Comput. Math. Math. Phys., 48:9 (2008), 1545–1569  isi  scopus
7. G. Yu. Kulikov, E. Yu. Khrustaleva, “Automatic step size and order control in explicit one-step extrapolation methods”, Zh. Vychisl. Mat. Mat. Fiz., 48:8 (2008),  1392–1405  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 48:8 (2008), 1313–1326  isi  scopus
2004
8. G. Yu. Kulikov, A. I. Merkulov, “On one-step collocation methods with higher derivatives for solving ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 44:10 (2004),  1782–1807  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 44:10 (2004), 1696–1720
9. G. Yu. Kulikov, S. K. Shindin, “On multistep methods of the interpolation type with an automated checking of the global error”, Zh. Vychisl. Mat. Mat. Fiz., 44:8 (2004),  1388–1409  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 44:8 (2004), 1314–1333
10. G. Yu. Kulikov, S. K. Shindin, “On the efficient computation of asymptotically sharp estimates for local and global errors in multistep methods with constant coefficients”, Zh. Vychisl. Mat. Mat. Fiz., 44:5 (2004),  840–861  mathnet  mathscinet; Comput. Math. Math. Phys., 44:5 (2004), 794–814
2002
11. G. Yu. Kulikov, “Implicit extrapolational methods for systems of differential-algebraic equations”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2002, 5,  3–7  mathnet  mathscinet  zmath
2001
12. G. Yu. Kulikov, A. A. Korneva, G. Ya. Benderskaya, “On numerical solution of large-scale systems of index 1 differential-algebraic equations”, Fundam. Prikl. Mat., 7:4 (2001),  1047–1080  mathnet  mathscinet  zmath
13. G. Yu. Kulikov, “On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1”, Zh. Vychisl. Mat. Mat. Fiz., 41:8 (2001),  1180–1189  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 41:8 (2001), 1122–1131
2000
14. G. Yu. Kulikov, “On symmetry of some Runge–Kutta methods”, Fundam. Prikl. Mat., 6:4 (2000),  1131–1140  mathnet  mathscinet  zmath
15. G. Yu. Kulikov, S. K. Shindin, “A technique for controlling the global error in multistep methods”, Zh. Vychisl. Mat. Mat. Fiz., 40:9 (2000),  1308–1329  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 40:9 (2000), 1255–1275
16. A. N. Andrianova, G. Yu. Kulikov, “On pseudodiagonally optimal Runge-Kutta simple iteration methods for systems of differential-algebraic equations of index $1$”, Zh. Vychisl. Mat. Mat. Fiz., 40:7 (2000),  1071–1089  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 40:7 (2000), 1027–1045
1998
17. G. Yu. Kulikov, “Asymptotic error estimates for the method of simple iteration and for the modified and generalized Newton methods”, Mat. Zametki, 63:4 (1998),  562–571  mathnet  mathscinet  zmath; Math. Notes, 63:4 (1998), 494–502  isi
18. G. Yu. Kulikov, “A method of error analysis for Runge–Kutta methods”, Zh. Vychisl. Mat. Mat. Fiz., 38:10 (1998),  1651–1653  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:10 (1998), 1580–1582
19. G. Yu. Kulikov, “Numerical solution of the Cauchy problem for a system of differential-algebraic equations with the use of implicit Runge–Kutta methods with a nontrivial predictor”, Zh. Vychisl. Mat. Mat. Fiz., 38:1 (1998),  68–84  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 38:1 (1998), 64–80
1997
20. G. Yu. Kulikov, “On the numerical solution of the Cauchy problem for a system of differential-algebraic equations by means of implicit Runge–Kutta methods with a variable integration step”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1997, 5,  7–11  mathnet  mathscinet  zmath
1996
21. G. Yu. Kulikov, “Convergence theorems for iterative Runge–Kutta methods with a constant integration step”, Zh. Vychisl. Mat. Mat. Fiz., 36:8 (1996),  73–89  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:8 (1996), 1041–1054  isi
1994
22. G. Yu. Kulikov, “Practical realization and efficiency of numerical methods for solving the Cauchy problem with an algebraic constraint”, Zh. Vychisl. Mat. Mat. Fiz., 34:11 (1994),  1617–1631  mathnet  mathscinet; Comput. Math. Math. Phys., 34:11 (1994), 1389–1401  isi
1993
23. G. Yu. Kulikov, “On the numerical solution of an autonomous Cauchy problem with an algebraic constraint on the phase variables (the nonsingular case)”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1993, 3,  10–14  mathnet  mathscinet  zmath
24. G. Yu. Kulikov, “The numerical solution of the autonomous Cauchy problem with algebraic constraints on the phase variables”, Zh. Vychisl. Mat. Mat. Fiz., 33:4 (1993),  522–540  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 33:4 (1993), 477–492  isi
1992
25. G. Yu. Kulikov, “A method for the numerical solution of the autonomous Cauchy problem with an algebraic restriction on the phase variables”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 1992, 1,  14–19  mathnet  mathscinet  zmath

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