Numerical methods;
initial value problem for ordinary differential equations; differential-algebraic systems,
global error estimation and control techniques; extended, unscented and cubature Kalman filters.
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:
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
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
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
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
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
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
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
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
G. Yu. Kulikov, “Cheap global error estimation in some Runge-Kutta pairs”, IMA Journal of Numerical Analysis, 33:1 (2013), 136-163
G.Yu. Kulikov, “Global error control in adaptive Nordsieck methods”, SIAM Journal on Scientific Computing, 34:2 (2012), A839-A860
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
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
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
G.Yu. Kulikov, “Proportional extrapolation and symmetric one-step methods”, Russian Journal of Numerical Analysis and Mathematical Modelling, 26:1 (2011), 49-73
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
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
G.Yu. Kulikov, “Local theory of extrapolation methods”, Numerical Algorithms, 53 (2010), 321-342
G.Yu. Kulikov, “On quasi-consistent integration by Nordsieck methods”, Journal of Computational and Applied Mathematics, 225:1 (2009), 268-287
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
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
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
G. Yu. Kulikov, “Nested implicit Runge–Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations”, Zh. Vychisl. Mat. Mat. Fiz., 60:7 (2020), 1170–1192; Comput. Math. Math. Phys., 60:7 (2020), 1134–1154
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; Num. Anal. Appl., 4:3 (2011), 199–209
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; Comput. Math. Math. Phys., 50:6 (2010), 1006–1023
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; Comput. Math. Math. Phys., 48:9 (2008), 1545–1569
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; Comput. Math. Math. Phys., 44:8 (2004), 1314–1333
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; Comput. Math. Math. Phys., 44:5 (2004), 794–814
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
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; Comput. Math. Math. Phys., 41:8 (2001), 1122–1131
G. Yu. Kulikov, “On symmetry of some Runge–Kutta methods”, Fundam. Prikl. Mat., 6:4 (2000), 1131–1140
16.
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; Comput. Math. Math. Phys., 40:9 (2000), 1255–1275
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; Comput. Math. Math. Phys., 40:7 (2000), 1027–1045
1998
18.
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; Math. Notes, 63:4 (1998), 494–502
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; Comput. Math. Math. Phys., 38:1 (1998), 64–80
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, no. 5, 7–11
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; Comput. Math. Math. Phys., 34:11 (1994), 1389–1401
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, no. 3, 10–14
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; Comput. Math. Math. Phys., 33:4 (1993), 477–492
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, no. 1, 14–19