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: https://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.

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                
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          
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          
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          
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          
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                
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          
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          
9. G. Yu. Kulikov, “Cheap global error estimation in some Runge-Kutta pairs”, IMA Journal of Numerical Analysis, 33:1 (2013), 136-163          
10. G.Yu. Kulikov, “Global error control in adaptive Nordsieck methods”, SIAM Journal on Scientific Computing, 34:2 (2012), A839-A860          
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          
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              
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          
14. G.Yu. Kulikov, “Proportional extrapolation and symmetric one-step methods”, Russian Journal of Numerical Analysis and Mathematical Modelling, 26:1 (2011), 49-73          
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          
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            
17. G.Yu. Kulikov, “Local theory of extrapolation methods”, Numerical Algorithms, 53 (2010), 321-342              
18. G.Yu. Kulikov, “On quasi-consistent integration by Nordsieck methods”, Journal of Computational and Applied Mathematics, 225:1 (2009), 268-287            
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            
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          
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            
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      

Publications in Math-Net.Ru

Personal pages:

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Organisations:

• Instituto Superior Técnico, Universidade de Lisboa
• Ulyanovsk State University, Faculty of Mathematics and Mechanics
• University of the Witwatersrand, Johannesburg