Papers in International Journals

• Kulikova, Maria; Kulikov, Gennady Yu (2024)  Maximum-correntropy-based sequential method for fast neural population activity reconstruction in the cortex from incomplete abnormally-disturbed noisy measurements . Communications in Nonlinear Science and Numerical Simulation: 139, 108266.

• Kulikova, Maria; Kulikov, Gennady Yu (2024)  Continuous-discrete derivative-free extended Kalman filter based on Euler-Maruyama and Itô-Taylor discretizations: Conventional and square-root implementations . European Journal of Control: 76, 100960.

• Kulikova, Maria; Taylor, David R.; Kulikov, Gennady Yu (2024)  Evolving efficiency of the BRICS markets . Economic Systems: 48(1), 101166.

• Kulikov, Gennady Yu; Kulikova, Maria (2024)  NIRK-based mixed-type accurate continuous-discrete Gaussian filters with deterministically sampled expectation and covariance for state estimation in continuous-time stochastic process models with discrete measurements . Journal of the Franklin Institute: 361(7), 106768.

• Kulikova, Maria; Kulikov, Gennady Yu (2024)  Euler-Maruyama-based data-driven state restoration and parameter adaptation in stochastic neural fields with finite signal transmission rate . IEEE Transactions on Information Theory: 70(6), 4571-4581.

• Kulikov, Gennady Yu; Kulikova, Maria (2023)  Accuracy analysis of numerical simulations and noisy data assimilations in two-dimensional stochastic neural fields with infinite signal transmission speed . Journal of the Franklin Institute: 360(1), 176-202.

• Kulikova, Maria; Kulikov, Gennady Yu (2023)  Data-driven parameter estimation in stochastic dynamic neural fields by state-space approach and continuous-discrete extended Kalman filtering . Digital Signal Processing: 136, 104010.

• Kulikova, Maria; Kulikov, Gennady Yu (2023)  On derivative-free extended Kalman filtering and its Matlab-oriented square-root implementations for state estimation in continuous-discrete nonlinear stochastic systems . European Journal of Control: 73, 100886.

• Kulikova, Maria; Kulikov, Gennady Yu (2022)  Estimation of market efficiency process within time-varying autoregressive models by extended Kalman filtering approach . Digital Signal Processing: 128, 103619.

• Kulikova, Maria; Kulikov, Gennady Yu (2022)  Continuous-discrete unscented Kalman filtering framework by MATLAB ODE solvers and square-root methods . Automatica: 141, 110396.

• Kulikov, Gennady Yu; Kulikova, Maria (2022)  Hyperbolic-SVD-based square-root unscented Kalman filters in continuous-discrete target tracking scenarios . IEEE Transactions on Automatic Control: 61(7), 366-373.

• Kulikov, Gennady Yu; Kulikova, Maria (2022)  Universal MATLAB-based square-root solutions in the family of continuous-discrete Gaussian filters for state estimation in nonlinear stochastic dynamic systems . International Journal of Robust and Nonlinear Control: 32(15), 8227-8251.

• Kulikov, Gennady Yu; Kulikova, Maria (2022)  Overall hyperbolic-singular-value-decomposition-based square-root solutions in Kalman filters with deterministically sampled mean and covariance for state estimation in continuous-discrete nonlinear stochastic systems . European Journal of Control: 66, 100648.

• Lima, Pedro M.; Erlhagen W.; Kulikova, Maria; Kulikov, Gennady Yu (2022)  Numerical solution of the stochastic neural field equation with applications to working memory . Physica A: Statistical Mechanics and its Applications: 596, 127166.

• Kulikova, Maria; Kulikov, Gennady Yu (2022)  Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter . Applied Numerical Mathematics: 171, 32-44.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Sequential method for fast neural population activity reconstruction in the cortex from incomplete noisy measurements . Computers in Biology and Medicine: 141: 105103.

• Kulikov, Gennady Yu; Kulikova, Maria (2021)  Itô-Taylor-based square-root unscented Kalman filtering methods for state estimation in nonlinear continuous-discrete stochastic systems . European Journal of Control: 58, 101-113.

• Kulikov, Gennady Yu; Kulikova, Maria (2021)  Square-root high-degree cubature Kalman filters for state estimation in nonlinear continuous-discrete stochastic systems . European Journal of Control: 59, 58-68.

• Kulikova, Maria; Tsyganova, J.V.; Kulikov, Gennady Yu (2021)  SVD-based state and parameter estimation approach for generalized Kalman filtering with application to GARCH-in-Mean estimation . Journal of Computational and Applied Mathematics: 387: 112487.

• Kulikov, Gennady Yu; Lima, Pedro M.; Kulikova, Maria (2021)  Numerical solution of the neural field equation in the presence of random disturbance. . Journal of Computational and Applied Mathematics: 387: 112563.

• Kulikova, Maria; Kulikov, Gennady Yu (2021)  MATLAB-based general approach for square-root extended-unscented and fifth-degree cubature Kalman filtering methods . European Journal of Control: 59, 1-12.

• Kulikova, Maria; Tsyganova, J.V.; Kulikov, Gennady Yu (2020)  UD-based pairwise and MIMO Kalman-like filtering for estimation of econometric model structures . IEEE Transactions on Automatic Control: 65(10), 4472-4479.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  Hyperbolic-singular-value-decomposition-based square-root accurate continuous-discrete extended-unscented Kalman filters for estimating continuous-time stochastic models with discrete measurements . International Journal of Robust and Nonlinear Control: 30(5), 2033-2058.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  The J-orthogonal square-root Euler-Maruyama-based unscented Kalman filter for nonlinear stochastic systems . IFAC-PapersOnLine: 53(2), 2361-2366.

• Kulikova, Maria; Kulikov, Gennady Yu (2020)  The J-orthogonal square-root MATLAB-based continuous-discrete unscented Kalman filtering method . IFAC-PapersOnLine: 53(2), 4967-4972.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  Square-root accurate continuous-discrete extended-unscented Kalman filtering methods with embedded orthogonal and J-orthogonal QR decompositions for estimation of nonlinear continuous-time stochastic models in radar tracking . Signal Processing: 166: 107253.

• Kulikov, Gennady Yu (2020)  Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations . Computational Mathematics and Mathematical Physics: 60(7), 1134-1154..

• Kulikova, Maria; Kulikov, Gennady Yu (2020)  SVD-based factored-form Cubature Kalman Filtering for continuous-time stochastic systems with discrete measurements . Automatica: 120: 109110.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  The J-orthogonal square-root fifth-degree cubature Kalman filtering method for nonlinear stochastic systems . IFAC-PapersOnLine: 53(2), 4961-4966.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  A comparative study of Kalman-like filters for state estimation of turning aircraft in presence of glint noise . IFAC-PapersOnLine: 53(2), 2335-2340.

• Kulikov, Gennady Yu; Kulikova, Maria (2020)  NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements . Applied Numerical Mathematics: 147, 196-221.

• Kulikova, Maria; Kulikov, Gennady Yu (2020)  Square-rooting approaches to accurate mixed-type continuous-discrete extended and fifth-degree cubature Kalman filters . IET Radar, Sonar & Navigation: 14(11), 1671-1680.

• Kulikov, Gennady Yu; Weiner, R. (2020)  Variable-stepsize doubly quasi-consistent singly diagonally implicit two-step peer pairs for solving stiff ordinary differential equations . Applied Numerical Mathematics: 154, 223-242.

• Kulikov, Gennady Yu; Taylor, D.R.; Kulikova, Maria (2019)  A nonlinear Bayesian filtering approach to estimating adaptive market efficiency . Russian Journal of Numerical Analysis and Mathematical Modelling: 34(1), 31-42.

• Kulikov, Gennady Yu; Kulikova, Maria (2019)  Numerical robustness of extended Kalman filtering based state estimation in ill-conditioned continuous-discrete nonlinear stochastic chemical systems . International Journal of Robust and Nonlinear Control: 29(5), 1377-1395.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Practical implementation of extended Kalman filtering in chemical systems with sparse measurements . Russian Journal of Numerical Analysis and Mathematical Modelling: 33(1), 41-53.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Stability analysis of extended, cubature and unscented Kalman filters for estimating stiff continuous-discrete stochastic systems . Automatica: 90, 91-97.

• Kulikov, Gennady Yu; Weiner, R. (2018)  Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods . Journal of Computational and Applied Mathematics: 340, 256-275.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Moore-Penrose-pseudo-inverse-based Kalman-like filtering methods for estimation of stiff continuous-discrete stochastic systems with ill-conditioned measurements . IET Control Theory & Applications: 12(16), 2205-2212.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Estimation of maneuvering target in the presence of non-Gaussian noise: a coordinated turn case study . Signal Processing: 145, 241-257.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Square-root Kalman-like filters for estimation of stiff continuous-time stochastic systems with ill-conditioned measurements . IET Control Theory and Applications: 11(9), 1420-1425.

• Weiner, R ; Kulikov, Gennady Yu; Beck, S.; Brud, J. (2017)  New third- and fourth-order singly diagonally implicit two-step peer triples with local and global error controls for solving stiff ordinary differential equations . Journal of Computational and Applied Mathematics: 316, 380-391.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements . Applied Numerical Mathematics: 111, 260-275.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Accurate continuous–discrete unscented Kalman filtering for estimation of nonlinear continuous-time stochastic models in radar tracking . Signal Processing: 139, 25-35.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Do the contemporary cubature and unscented Kalman filtering methods outperform always the extended Kalman filter? . IFAC-PapersOnLine: 50(1), 3762-3767.

• Kulikova, Maria; Kulikov, Gennady Yu (2017)  NIRK-based accurate continuous-discrete extended Kalman filters for estimating continuous-time stochastic target tracking models . Journal of Computational and Applied Mathematics: 316, 260-270.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  The continuous-discrete extended Kalman filter revisited . Russian Journal of Numerical Analysis and Mathematical Modelling: 32(1), 27-38.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Accurate state estimation in continuous-discrete stochastic state-space systems with nonlinear or nondifferentiable observations . IEEE Transactions on Automatic Control: 43(8), 4243-4250.

• Kulikov, Gennady Yu; Kulikova, Maria (2017)  Accurate state estimation of stiff continuous-time stochastic models in chemical and other engineering . Mathematics and Computers in Simulation: 142, 62-81.

• Kulikov, Gennady Yu; Kulikova, Maria (2016)  The accurate continuous-discrete extended Kalman filter for radar tracking . IEEE Transactions on Signal Processing: 64(4), 948-958.

• Kulikov, Gennady Yu; Kulikova, Maria (2016)  Estimating the state in stiff continuous-time stochastic systems within extended Kalman filtering . SIAM Journal on Scientific Computing: 38(6), A3565-A3588.

• Kulikov, Gennady Yu; Kulikova, Maria (2015)  The accurate continuous-discrete extended Kalman filter for continuous-time stochastic systems . Russian Journal of Numerical Analysis and Mathematical Modelling: 30(4), 239-249.

• Kulikov, Gennady Yu (2015)  Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems . Computational Mathematics and Mathematical Physics: 55(6), 983-1003.

• Kulikov, Gennady Yu; Weiner, R. (2015)  A singly diagonally implicit two-step peer triple with global error control for stiff ordinary differential equations . SIAM Journal on Scientific Computing: 37(3), A1593–A1613.

• Kulikov, Gennady Yu; Kulikova, Maria (2015)  High-order accurate continuous-discrete extended Kalman filter for chemical engineering . European Journal of Control: 21, 14-26.

• Weiner, R.; Kulikov, Gennady Yu (2014)  Local and Global Error Estimation and Control Within Explicit Two-Step Peer Triples . Journal of Computational and Applied Mathematics: 262, 261-270.

• Kulikov, Gennady Yu; Lima, Pedro M.; Morgado, M. Luísa (2014)  Analysis and Numerical Approximation of Singular Boundary Value Problems with the P-Laplacian in Fluid Mechanics . Journal of Computational and Applied Mathematics: 262, 87-104.

• Weiner, R.; Kulikov, Gennady Yu (2014)  Efficient Error Control in Numerical Integration of Ordinary Differential Equations and Optimal Interpolating Variable-Stepsize Peer Methods . Computational Mathematics and Mathematical Physics: 54(4), 604-619.

• Kulikova, Maria; Kulikov, Gennady Yu (2014)  Adaptive ODE Solvers in Extended Kalman Filtering Algorithms . Journal of Computational and Applied Mathematics: 262, 205-216.

• Kulikov, Gennady Yu; Kulikova, Maria (2014)  Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter . IEEE Transactions on Automatic Control: 59(1), 273-279.

• Kulikov, Gennady Yu (2013)  Adaptive Nordsieck Formulas with Advanced Global Error Control Mechanisms . Russian Journal of Numerical Analysis and Mathematical Modelling: 28(4), 321-352.

• Kulikov, Gennady Yu (2013)  Cheap global error estimation in some Runge-Kutta pairs . IMA Journal of Numerical Analysis: 33(1), 136-163.

• Weiner, R.; Kulikov, Gennady Yu; Podhaisky, H. (2012)  Variable-Stepsize Doubly Quasi-Consistent Parallel Explicit Peer Methods with Global Error Control . Applied Numerical Mathematics: 62(10), 1591-1603.

• Kulikov, Gennady Yu (2012)  Global Error Control in Adaptive Nordsieck Methods . SIAM Journal on Scientific Computing: 34(2), A839-A860.

• Kulikov, Gennady Yu (2012)  Solving the Order Reduction Phenomenon in Variable Step Size Quasi-Consistent Nordsieck Methods . Computational Mathematics and Mathematical Physics: 52(11), 1547-1564.

• Kulikov, Gennady Yu; Weiner, R. (2011)  Global Error Estimation and Control in Linearly-Implicit Parallel Two-Step Peer W-Methods . Journal of Computational and Applied Mathematics: 236(6), 1226-1239.

• Kulikov, Gennady Yu; Kuznetsov, E.B.; Khrustaleva, E.Yu. (2011)  On the global error control in nested implicit Runge-Kutta methods of Gauss type . Numerical Analysis and Applications: 14(3), 245-259.

• Kulikov, Gennady Yu (2011)  Proportional Extrapolation and Symmetric One-Step Methods . Russian Journal of Numerical Analysis and Mathematical Modelling: 26(1), 49-73.

• Kulikov, Gennady Yu; Weiner, R. (2010)  Variable-Stepsize Interpolating Explicit Parallel Peer Methods with Inherent Global Error Control . SIAM Journal on Scientific Computing: 32(4), 1695-1723.

• Kulikov, Gennady Yu; Weiner, R. (2010)  Doubly Quasi-Consistent Parallel Explicit Peer Methods with Built-In Global Error Estimation . Journal of Computational and Applied Mathematics: 233(9), 2351-2364.

• Kulikov, Gennady Yu; Khrustaleva, E. Yu. (2010)  Automatic Step Size and Order Control in One-Step Collocation Methods with Higher Derivatives . Computational Mathematics and Mathematical Physics: 50(6), 1006-1023.

• Kulikov, Gennady Yu (2010)  Local Theory of Extrapolation Methods . Numerical Algorithms: 53(2-3), 321-342.

• Kulikov, Gennady Yu; Weiner, R. (2010)  Global Error Control in Implicit Parallel Peer Methods . Russian Journal of Numerical Analysis and Mathematical Modelling: 25(2), 131-146.

• Kulikov, Gennady Yu (2009)  On quasi-consistent integration by Nordsieck methods . Journal of Computational and Applied Mathematics: 225, 268-287.

• Kulikov, Gennady Yu; Shindin, S.K. (2009)  Adaptive nested implicit Runge-Kutta formulas of Gauss type . Applied Numerical Mathematics: 59, 707-722.

• Kulikov, Gennady Yu (2009)  Automatic error control in the Gauss-type nested implicit Runge-Kutta formula of order 6 . Russian Journal of Numerical Analysis and Mathematical Modelling: 24(2), 123-144.

• Kulikov, Gennady Yu; Khrustaleva, E.Yu. (2008)  Automatic step size and order control in implicit one-step extrapolation methods . Computational Mathematics and Mathematical Physics: 48(9), 1545-1569.

• Kulikov, Gennady Yu; Khrustaleva, E.Yu. (2008)  Automatic step size and order control in explicit one-step extrapolation methods . Computational Mathematics and Mathematical Physics: 48(8), 1313-1326.

• Kulikov, Gennady Yu; Shindin, S.K. (2008)  Local and global error estimation in Nordsieck methods . Russian Journal of Numerical Analysis and Mathematical Modelling: 23(6), 567-595.

• Kulikov, Gennady Yu; Merkulov, A.I.; Shindin, S.K. (2007)  Asymptotic error estimate for general Newton-type methods and its application to differential equations . Russian Journal of Numerical Analysis and Mathematical Modelling: 22(6), 567-590.

• Kulikov, Gennady Yu; Shindin, S.K.  (2007)  Numerical tests with Gauss-type nested implicit Runge-Kutta formulas . Lecture Notes in Computer Science: 4487, 136-143.

• Kulikov, Gennady Yu; Shindin, S.K. (2006)  On a family of cheap symmetric one-step methods of order four . Lecture Notes in Computer Science: 3991, 781-785.

• Kulikov, Gennady Yu; Shindin, S.K.  (2006)  One-leg variable-coefficient formulas for ordinary differential equations and the local-global step size control . Numerical Algorithms: 43(1), 99-121.

• Kulikov, Gennady Yu; Khrustaleva, E.Yu.; Merkulov, A.I. (2006)  Symmetric Runge-Kutta methods with higher derivatives and quadratic extrapolation . Lecture Notes in Computer Science: 3991, 117-123.

• Kulikov, Gennady Yu; Shindin, S.K. (2006)  Nordsieck methods on nonuniform grids: Stability and order reduction phenomenon . Mathematics and Computers in Simulation: 72(1), 47-56.

• Kulikov, Gennady Yu; Shindin, S.K.  (2005)  On stable integration of stiff ordinary differential equations with global error control . Lecture Notes in Computer Science: 3514, 42-49.

• Kulikov, Gennady Yu; Shindin, S.K.  (2005)  One-leg integration of ordinary differential equations with global error control . Computational Methods in Applied Mathematics: 5(1), 86-96.

• Kulikov, Gennady Yu; Shindin, S.K. (2005)  Global error estimation and extrapolated multistep methods for index 1 differential-algebraic systems . BIT Numerical Mathematics: 45(3), 517-542.

• Kulikov, Gennady Yu; Shindin, S.K. (2004)  On automatic global error control in multistep methods with polynomial interpolation of numerical solution . Lecture Notes in Computer Science: 3045, 345-354.

• Kulikov, Gennady Yu (2004)  One-step methods and implicit extrapolation technique for index 1 differential-algebraic systems . Russian Journal of Numerical Analysis and Mathematical Modelling: 19(6), 527-553.

• Kulikov, Gennady Yu; Shindin, S.K. (2004)  On multistep interpolation-type methods with automatic global error control . Computational Mathematics and Mathematical Physics: 44(8), 1314-1333.

• Kulikov, Gennady Yu; Merkulov, A.I.; Khrustaleva, E.Yu. (2004)  On a family of A-stable collocation methods with high derivatives . Lecture Notes in Computer Science: 3037, 73-80.

• Kulikov, Gennady Yu; Shindin, S.K. (2004)  INTEGRATOR: A computational tool to solve ordinary differential equations with global error control . Lecture Notes in Computer Science: 3037, 570-573.

• Kulikov, Gennady Yu; Merkulov, A.I. (2004)  Asymptotic error estimate of iterative Newton-type methods and its practical application . Lecture Notes in Computer Science: 3045, 667-675.

• Kulikov, Gennady Yu; Shindin, S.K. (2004)  On an effective computation of asymptotically correct estimates of the local and global errors for multistep methods with fixed coefficients . Computational Mathematics and Mathematical Physics: 44(5), 794-814.

• Kulikov, Gennady Yu; Merkulov, A.I. (2004)  On one-step collocation methods with higher derivatives for solving ordinary differential equations . Computational Mathematics and Mathematical Physics: 44(10), 1696-1720.

• Kulikov, Gennady Yu (2004)  An advanced version of the local-global step size control for Runge-Kutta methods applied to index 1 differential-algebraic systems . Lecture Notes in Computer Science: 3037, 565-569.

• Kulikov, Gennady Yu (2003)  Symmetric Runge-Kutta methods and their stability . Russian Journal of Numerical Analysis and Mathematical Modelling: 18(1), 13-41.

• Kulikov, Gennady Yu; Shindin, S.K. (2003)  Extrapolated multistep methods and local-global step size control . Lecture Notes in Computer Science: 2657, 540-549.

• Kulikov, Gennady Yu (2003)  On the stability of symmetric Runge-Kutta formulas . Doklady Mathematics: 67(2), 184-188.

• Kulikov, Gennady Yu (2002)  On implicit extrapolation methods for ordinary differential equations . Russian Journal of Numerical Analysis and Mathematical Modelling: 17(1), 41-69.

• Kulikov, Gennady Yu (2002)  On the use of Hotelling's iterations for solving differential-algebraic systems of index 1 . Doklady Mathematics: 66(3), 348-352.

• Kulikov, Gennady Yu (2002)  On implicit extrapolation methods for systems of differential-algebraic equations . Moscow University Mathematics Bulletin: 57(5), 1-5.

• Kulikov, Gennady Yu; Benderskaya, G.Ya. (2002)  On implementation of vector Gauss method for solving large-scale systems of index 1 differential-algebraic equations . Lecture Notes in Computer Science: 2330, 412-421.

• Kulikov, Gennady Yu (2001)  On using Newton-type iterative methods for solving systems of differential-algebraic equations of index 1 . Computational Mathematics and Mathematical Physics: 41(8), 1122-1131.

• Kulikov, Gennady Yu; Korneva, A.A. (2001)  On efficient application of implicit Runge-Kutta methods to large-scale systems of index 1differential-algebraic equations . Lecture Notes in Computer Science: 2073, 832-841.

• Kulikov, Gennady Yu; Shindin, S.K.  (2000)  On multistep extrapolation methods for ordinary differential equations . Doklady Mathematics: 61(3), 357-360.

• Kulikov, Gennady Yu (2000)  A local-global version of a stepsize control for Runge-Kutta methods . Journal of Applied Mathematics and Computing: 7(2), 289-318.

• Kulikov, Gennady Yu; Shindin, S.K. (2000)  A technique for controlling the global error in multistep methods . Computational Mathematics and Mathematical Physics: 40(9), 1255-1275.

• Andrianova, N.A.; Kulikov, Gennady Yu (2000)  On pseudodiagonally optimal Runge-Kutta simple iteration methods for systems of differential- algebraic equations of index 1 . Computational Mathematics and Mathematical Physics: 40(7), 1027-1045.

• Kulikov, Gennady Yu; Shindin, S.K. (1999)  A local-global stepsize control for multistep methods applied to semi-explicit index 1 differential-algebraic equations . Journal of Applied Mathematics and Computing: 6(3), 463-492.

• Kulikov, Gennady Yu (1998)  Revision of the theory of symmetric one-step methods for ordinary differential equations . Journal of Applied Mathematics and Computing: 5(3), 579-600.

• Kulikov, Gennady Yu (1998)  Asymptotic error estimates for the method of simple iterations and for the modified and generalized Newton methods . Mathematical Notes: 63(3-4), 494-502.

• Kulikov, Gennady Yu (1998)  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 . Computational Mathematics and Mathematical Physics: 38(1), 64-80.

• Kulikov, Gennady Yu (1998)  A method of error analysis for Runge-Kutta methods . Computational Mathematics and Mathematical Physics: 38(10), 1580-1582.

• Kulikov, Gennady Yu (1997)  A theory of symmetric one-step methods for differential-algebraic equations . Russian Journal of Numerical Analysis and Mathematical Modelling: 12(6), 501-523.

• Kulikov, Gennady Yu (1997)  Numerical methods solving the semi-explicit differential-algebraic equations by implicit multistep fixed stepsize methods . Journal of Applied Mathematics and Computing: 4(2), 281-318.

• Kulikov, Gennady Yu (1997)  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 . Moscow University Mathematics Bulletin: 52(5), 6-10.

• Kulikov, Gennady Yu (1996)  Convergence theorems for iterative Runge-Kutta methods with a constant integration step . Computational Mathematics and Mathematical Physics: 36(8), 1041-1054.

• Kulikov, Gennady Yu (1994)  The practical implementation and efficiency of the numerical methods for solving the Cauchy problem with an algebraic relation between the phase variables . Computational Mathematics and Mathematical Physics: 34(11), 1389-1401.

• Kulikov, Gennady Yu (1993)  The numerical solution of the autonomous Cauchy problem with an algebraic relation between the phase variables . Computational Mathematics and Mathematical Physic: 33(4), 477-492.

• Kulikov, Gennady Yu (1993)  The numerical solution of an autonomous Cauchy problem with an algebraic constraint on the phase variables (the nonsingular case) . Moscow University Mathematics Bulletin: 48(3), 8-12.

• Kulikov, Gennady Yu (1992)  A method for the numerical solution of the autonomous Cauchy problem with an algebraic restriction of the phase variables . Moscow University Mathematics Bulletin: 47(1), 14-18.

Books

• Kulikov, Gennady Yu; Kulikova, Maria (2024)  State Estimation for Nonlinear Continuous-Discrete Stochastic Systems: Numerical Aspects and Implementation Issues . Springer, Cham, 780 p. Hardcover ISBN: 978-3-031-61370-8, Softcover ISBN: 978-3-031-61373-9, eBook ISBN: 978-3-031-61371-5..

• Semoushin, I.V.; Kulikov, Gennady Yu (2000)  Computational Linear Algebra: Collected Assignments for Laboratory Case Studies, Tests and Examinations . Ulyanovsk State Technical University, Ulyanovsk: ISBN 5-89146-139-0, 119 p. (In Russian).

• Shakin, V.V.; Komissarov, K.V.; Kulikov, Gennady Yu; Tsitovtsev, V.E.; Shapoval, A.V.; Schirov, A.V.; Goloveschenkov, O.V.; Panfilov, A.V.; Strizhov, V.V.; Przhialkovsky, V.V. (1996)  Biosystems under extreme conditions . Computing Center, Russian Academy of Sciences, Moscow: ISBN 5-201-09728-6, 84 p. (In Russian).

Communications in Conference Proceedings

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Pattern Recognition Facilities of Extended Kallman Filtering in Stochastic Neural Fields . Proceedings of ECC2022, 1436-1441.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2022)  Accurate Ito-Taylor-Discretization-Based State Estimation in Stochastic Neural Field Equations with Infinte Signal Transmissiion Rate . Proceedings of ECC2022, 1436-1441.

• Kulikov, Gennady Yu; Kulikova, Maria (2021)  Self-adaptive MATLAB-based Gauss-Hermite quadrature filter for state estimation in nonlinear continuous-discrete stochastic systems . Proceedings of European Control Conference, Rotterdam, Netherlands, 848-853.

• Kulikova, Maria; Taylor, D.R.; Kulikov, Gennady Yu (2021)  Estimating a degree of evolving market efficiency: How efficient is the Romanian stock market? . Proceedings of the 25th International Conference on System Theory, Control and Computing, Iasi, Romania, 665-670.

• Kulikova, Maria; Lima, Pedro M.; Kulikov, Gennady Yu (2021)  Reconstruction of hidden states in stochastic neural field equations with infinite signal transmission rate . Proceedings of the 25th International Conference on System Theory, Control and Computing, Iasi, Romania, 358-365.

• Lima, Pedro M.; Erlhagen, W.; Kulikov, Gennady Yu; Kulikova, Maria (2021)  Mathematical modeling of working memory in the presence of random disturbance using neural field equations . Proceedings of V International Conference "Modeling of Nonlinear Processes and Systems" (MNPS-2020). EPJ Web of Conferences: 248, 01021.

• Kulikova, Maria; Kulikov, Gennady Yu; Lima, Pedro M. (2020)  Accuracy study in numerical simulations to stochastic neural field equations . Proceedings of the 24th International Conference on System Theory, Control and Computing, Sinaia, Romania, 254-261.

• Kulikova, Maria; Kulikov, Gennady Yu; Lima, Pedro M. (2019)  Effective Numerical Solution to Two-Dimensional Stochastic Neural Field Equations. . Proceedings of the 23rd International Conference on System Theory, Control and Computing, 650-655.

• Kulikov, Gennady Yu; Kulikova, Maria (2019)  SVD-based factored-form extended Kalman filters for state estimation in nonlinear continuous-discrete stochastic systems . Proceedings of the 23rd International Conference on System Theory, Control and Computing, Sinaia, Romania, 137-142.

• Kulikov, Gennady Yu; Kulikova, Maria; Lima, Pedro M. (2019)  Numerical Simulation of Neural Fields with Finite Transmission Speed and Random Disturbance . Proceedings of the 23rd International Conference on System Theory,, 644-649.

• Kulikov, Gennady Yu; Kulikova, Maria (2019)  The J-orthogonal square-root NIRK-based Extended-Unscented Kalman filter for nonlinear continuous-discrete stochastic systems . Proceedings of the 58-th IEEE Conference on Decision and Control, IEEE-CDC 2019. Nice, France, 373-378.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Numerical stability of EKF-based software sensors in chemical engineering: A Van Der Vusse reaction case study . Proceedings of the 22nd International Conference on System Theory, Control and Computing, Sinaia, Romania, 286-291.

• Kulikov, Gennady Yu; Kulikova, Maria (2018)  Accuracy issues in Kalman filtering state estimation of stiff continuous-discrete stochastic models arisen in engineering research . Proceedings of the 22nd International Conference on System Theory, Control and Computing, Sinaia, Romania, 800-805.

• Kulikova, Maria; Tsyganova, J.V.; Kulikov, Gennady Yu (2018)  SVD-based state estimation of pairwise Markov models with application in econometrics . Proceedings of the 22nd International Conference on System Theory, Control and Computing, Sinaia, Romania, 188-193.

• Kulikova, Maria; Kulikov, Gennady Yu (2016)  On computational robustness of accurate continuous-discrete unscented Kalman filtering for target tracking models . Proceedings 15th Annual European Control Conference, ECC 2016, Aalborg, Denmark, July 29 - June 1.

• Kulikov, Gennady Yu; Kulikova, Maria (2016)  Accurate continuous-discrete extended Kalman filtering for stiff continuous-time stochastic models in chemical engineering . Proceedings of European Control Conference, Aalborg, Denmark, 1728-1733.

• Kulikova, Maria; Kulikov, Gennady Yu (2015)  A mixed-type accurate continuous-discrete extended-unscented Kalman filter for target tracking . Proceedings of the 2015 European Control Conference (ECC 2015), Linz, Austria, 2824–2829.

• Kulikov, Gennady Yu; Kulikova, Maria (2015)  State estimation in chemical systems with infrequent measurements . Proceedings of the 2015 European Control Conference (ECC 2015), Linz, Austria, 2688–2693.

• Kulikov, Gennady Yu; Kulikova, Maria (2014)  Accurate state estimation in the Van der Vusse reaction . Proceedings of the IEEE 2014 Multi-Conference on Systems and Control, Antibes, France, 8-10 October, 759-764.

• Kulikova, Maria; Kulikov, Gennady Yu (2013)  Square-root accurate continuous-discrete extended Kalman filter for target tracking . Proceedings of the 52-nd IEEE Conference on Decision and Control, IEEE-CDC 2013, Florence, Italy, 7785-7790.

• Kulikov, Gennady Yu (2003)  Theory of implicit extrapolation methods for ordinary differential equations . Proceedings of the Numerical Mathematics and Advanced Applications (ENUMATH 2001) conference. Springer-Verlag Italia, Milano: ISBN 88-470-0180-3, 909-918.

• Kulikov, Gennady Yu; Benderskaya, G.Ya. (2002)  Effective numerical solution of large-scale index 1 differential-algebraic systems . Proceedings of the International Conference on Computational Mathematics (ICCM 2002): ICMMG Publisher, Novosibirsk, Russia: ISBN 5-901548-10-8, 561-566.

• Kulikov, Gennady Yu; Shindin, S.K. (2002)  An advanced version of local-global step size control for multistep methods . Proceedings of the International Conference on Computational Mathematics (ICCM 2002): Part II. ICMMG Publisher, Novosibirsk, Russia: ISBN 5-901548-10-8, 567-573.

• Kulikov, Gennady Yu; Shindin, S.K. (2000)  An advanced local-global stepsize control for multistep methods . Proceedings of the 3rd European Conference. World Scientific, Singapore: ISBN 981-02-4381-1, 593 - 600.

Thesis

• Kulikov, Gennady Yu (2002)  Numerical methods with global error control for solving differential and differential-algebraic equations of index 1 . Dissertation of Doctor of Sciences in Physics and Mathematics. Ulyanovsk State University, Ulyanovsk, 315 p. (In Russian).

• Kulikov, Gennady Yu (1994)  The numerical solution of the Cauchy problem with algebraic constraints on the phase variables (with applications in medical cybernetics) . Dissertation of Candidate of Sciences in Physics and Mathematics. Computing Center, Russian Academy of Sciences, Moscow, 197 p. (In Russian).

Papers in National Scientific Journals

• Kulikova, Maria; Kulikov, Gennady Yu (2016)  Numerical methods for nonlinear filtering of signals and measurements . Computational Technologies: 21(4), 64-98.

• Kulikov, Gennady Yu; Korneva, A.A.; Benderskaya, G.Ya. (2001)  On numerical solution of large-scale systems of index 1 differential-algebraic equations . Fundamental and Applied Mathematics: 7(4), 1047-1080 (In Russian).

• Kulikov, Gennady Yu (2000)  On symmetry of some Runge-Kutta methods . Fundamental and Applied Mathematics: 6(4), 1131-1140 (In Russian).