Search Results - Nested implicit Runge–Kutta formulas with global error control

On global error control in nested implicit Runge-Kutta methods of the gauss type.

Authors: Kulikov, G. Kuznetsov, E. Khrustaleva, E.

Source: Numerical Analysis & Applications; Jul2011, Vol. 4 Issue 3, p199-209, 11p

Nested Implicit Runge–Kutta Pairs of Gauss and Lobatto Types with Local and Global Error Controls for Stiff Ordinary Differential Equations.

Authors: Kulikov, G. Yu.

Source: Computational Mathematics & Mathematical Physics; Jul2020, Vol. 60 Issue 7, p1134-1154, 21p

Subject Terms: APPLIED mathematics, COMPUTATIONAL mathematics, NUMERICAL integration, ORDINARY differential equations, DESIGN techniques

Automatic error control in the Gauss-type nested implicit Runge–Kutta formula of order 6.

Authors: KULIKOV, G. Yu.

Source: Russian Journal of Numerical Analysis & Mathematical Modelling; 2009, Vol. 24 Issue 2, p123-144, 22p, 9 Charts, 1 Graph

Subject Terms: ERROR analysis in mathematics, NUMERICAL analysis, ERROR functions, EQUATIONS, DIFFERENTIAL equations, PARTIAL differential equations

Analysis and numerical approximation of singular boundary value problems with the -Laplacian in fluid mechanics.

Authors: Kulikov, G.Yu. Lima, P.M. Morgado, M.L.

Source: Journal of Computational & Applied Mathematics. May2014, Vol. 262, p87-104. 18p.

Subject Terms: *BOUNDARY value problems, *LAPLACIAN matrices, *FLUID mechanics, *NUMERICAL analysis, *ASYMPTOTIC expansions, *NUMERICAL integration

Accurate state estimation of stiff continuous-time stochastic models in chemical and other engineering.

Authors: Kulikov, G.Yu. Kulikova, M.V.

Source: Mathematics & Computers in Simulation. Dec2017, Vol. 142, p62-81. 20p.

Subject Terms: *STOCHASTIC models, *KALMAN filtering, *RUNGE-Kutta formulas, *DISCRETIZATION methods, *CHEMICAL engineering

NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements.

Authors: Kulikov, G.Yu. Kulikova, M.V.

Source: Applied Numerical Mathematics. Jan2020, Vol. 147, p196-221. 26p.

Subject Terms: *KALMAN filtering, *STOCHASTIC processes, *DISCRETE-time systems, *NONLINEAR estimation, *AIR traffic control, *STOCHASTIC systems, *STOCHASTIC models

NIRK-based accurate continuous–discrete extended Kalman filters for estimating continuous-time stochastic target tracking models.

Authors: Kulikova, M.V. Kulikov, G.Yu.

Source: Journal of Computational & Applied Mathematics. May2017, Vol. 316, p260-270. 11p.

Subject Terms: *KALMAN filtering, *STOCHASTIC analysis, *AUTOMATIC tracking, *DIFFERENTIAL equations, *NUMERICAL analysis

ESTIMATING THE STATE IN STIFF CONTINUOUS-TIME STOCHASTIC SYSTEMS WITHIN EXTENDED KALMAN FILTERING.

Authors: KULIKOV, G. YU. KULIKOVA, M. V.

Source: SIAM Journal on Scientific Computing; 2016, Vol. 38 Issue 6, pA3565-A3588, 24p

Subject Terms: STOCHASTIC systems, KALMAN filtering

Automatic step size and order control in one-step collocation methods with higher derivatives.

Authors: Kulikov, G. Khrustaleva, E.

Source: Computational Mathematics & Mathematical Physics; Jun2010, Vol. 50 Issue 6, p1006-1023, 18p

Accurate Numerical Implementation of the Continuous-Discrete Extended Kalman Filter.

Authors: Kulikov, Gennady Yu. Kulikova, Maria V.

Source: IEEE Transactions on Automatic Control; Jan2014, Vol. 59 Issue 1, p273-279, 7p

Subject Terms: CONTINUOUS functions, DISCRETE systems, KALMAN filtering, NUMERICAL analysis, PROBLEM solving, DIFFERENTIAL equations

Hydrological 0D and 2D Modelling of the Navio-Quebrado Coastal Lagoon (La Guajira, Colombia): A Challenging Exercise.

Authors: Nardini, Andrea Gianni Cristoforo Torres-Bejarano, Franklin Escobar Villanueva, Jairo R. et al.

Source: Water (20734441); Mar2025, Vol. 17 Issue 5, p636, 29p

Subject Terms: HYDROLOGIC models, LAGOONS, SIMULATION methods & models, BASIC needs, MATHEMATICAL models

Practical implementation of extended Kalman filtering in chemical systems with sparse measurements.

Authors: Kulikov, Gennady Yu. Kulikova, Maria V.

Source: Russian Journal of Numerical Analysis & Mathematical Modelling; 2018, Vol. 33 Issue 1, p41-53, 13p

Subject Terms: ALGORITHMIC randomness, RECURSION theory, ALGORITHMS, MACHINE translating, MACHINE theory

Numerical Approximation of Stiff Problems Using Efficient Nested Implicit Runge-Kutta Methods.

Authors: Ur-Rehman, Attique Ur Rehman, Shafiq Ahmad, Junaid

Source: Punjab University Journal of Mathematics; 2019, Vol. 51 Issue 2, p1-19, 19p

Subject Terms: APPROXIMATION theory, STIFF equations (Differential equations), IMPLICIT functions, RUNGE-Kutta formulas, GAUSS error function, ORDINARY differential equations

Cheap global error estimation in some Runge–Kutta pairs.

Authors: Kulikov, Gennady Yu.

Source: IMA Journal of Numerical Analysis; Jan2013, Vol. 33 Issue 1, p136-163, 28p

Subject Terms: ERROR analysis in mathematics, ESTIMATION theory, RUNGE-Kutta formulas, CONTROL theory (Engineering), ORDINARY differential equations, EMBEDDINGS (Mathematics)

Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems.

Authors: Kulikov, G.

Source: Computational Mathematics & Mathematical Physics; Jun2015, Vol. 55 Issue 6, p983-1003, 21p

Subject Terms: EMBEDDED computer systems, MATHEMATICAL symmetry, RUNGE-Kutta formulas, ORDINARY differential equations, HAMILTONIAN systems

PottsMGNet: A Mathematical Explanation of Encoder-Decoder Based Neural Networks.

Authors: Xue-Cheng Tai Hao Liu Chan, Raymond

Source: SIAM Journal on Imaging Sciences; 2024, Vol. 17 Issue 1, p540-594, 55p

A structural response reconstruction method based on a continuous-discrete state space model.

Authors: Chen, Fanghua Peng, Zhenrui

Source: Journal of Mechanical Science & Technology; Nov2023, Vol. 37 Issue 11, p5713-5723, 11p

Subject Terms: STRUCTURAL health monitoring, TIKHONOV regularization, INVERSE problems, KALMAN filtering, MATRIX inversion, RUNGE-Kutta formulas, SQUARE root, DISCRETE wavelet transforms

Numerical Tests with Gauss-Type Nested Implicit Runge-Kutta Formulas.

Authors: Hutchison, David Kanade, Takeo Kittler, Josef et al.

Source: Computational Science: ICCS 2007; 2007, p136-143, 8p

Testing a New Conservative Method for Solving the Cauchy Problem for Hamiltonian Systems on Test Problems.

Authors: Aleksandrov, P. A. Elenin, G. G.

Source: Computational Mathematics & Mathematical Physics; Sep2020, Vol. 60 Issue 9, p1422-1444, 23p

Subject Terms: KEPLER problem, TEST systems, RUNGE-Kutta formulas, ENERGY conservation, CAUCHY problem, PROBLEM solving, HAMILTONIAN systems

The continuous-discrete extended Kalman filter revisited.

Authors: Kulikov, Gennady Yu. Kulikova, Maria V.

Source: Russian Journal of Numerical Analysis & Mathematical Modelling; Feb2017, Vol. 32 Issue 1, p27-38, 12p

Subject Terms: NONLINEAR functions, NONLINEAR functional analysis, KALMAN filtering, STOCHASTIC analysis, DISCRETE choice models