Search Results - Nested implicit Runge–Kutta formulas

Adaptive nested implicit Runge–Kutta formulas of Gauss type

Authors: Sergey Shindin G. Yu. Kulikov

Source: Applied Numerical Mathematics. 59:707-722

Subject Terms: 0101 mathematics, 01 natural sciences

Access URL: https://dl.acm.org/citation.cfm?id=1498003
https://dl.acm.org/doi/10.1016/j.apnum.2008.03.019
https://www.sciencedirect.com/science/article/pii/S0168927408000573
https://www.math.tecnico.ulisboa.pt/~plima/projecto2009a/A5.pdf
http://www.math.ist.utl.pt/~plima/projecto2009a/A5.pdf

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

Authors: Sergey Shindin Gennady Yu. Kulikov

Source: Lecture Notes in Computer Science ISBN: 9783540725831

Access URL: https://link.springer.com/content/pdf/10.1007%2F978-3-540-72584-8_18.pdf
https://link.springer.com/10.1007/978-3-540-72584-8_18
https://dblp.uni-trier.de/db/conf/iccS/iccS2007-1.html#KulikovS07
https://link.springer.com/content/pdf/10.1007%2F978-3-540-72584-8_18.pdf
https://rd.springer.com/chapter/10.1007/978-3-540-72584-8_18
https://link.springer.com/chapter/10.1007%2F978-3-540-72584-8_18

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

Authors: G. Yu. Kulikov

Source: Russian Journal of Numerical Analysis and Mathematical Modelling. 24

Subject Terms: 0101 mathematics, 01 natural sciences

Access URL: https://www.degruyter.com/view/j/rnam.2009.24.issue-2/rjnamm.2009.009/rjnamm.2009.009.xml

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

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

Authors: Kulikov, G.¹ gkulikov@math.ist.utl.pt

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

Efficient Nested Implicit Runge--Kutta Methods for Nonlinear Stiff Problems.

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

Source: Punjab University Journal of Mathematics; 2019, Vol. 51 Issue 6, p33-51, 19p

Subject Terms: RUNGE-Kutta formulas, NUMERICAL analysis, GAUSSIAN quadrature formulas, MATHEMATICAL models, DIFFERENTIAL equations

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

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

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

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

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

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

Multiscale Nested Simulations of Rayleigh-Taylor Instabilities in Ionospheric Flows.

Authors: Mahalov, Alex Moustaoui, Mohamed

Source: Journal of Fluids Engineering. Jun2014, Vol. 136 Issue 6, p1-8. 8p.

Subject Terms: Ionospheric plasma, Rayleigh-Taylor instability, Equatorial spread F, Ions, Runge-Kutta formulas

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

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 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

Moore‐Penrose‐pseudo‐inverse‐based Kalman‐like filtering methods for estimation of stiff continuous‐discrete stochastic systems with ill‐conditioned measurements.

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

Source: IET Control Theory & Applications (Wiley-Blackwell); Nov2018, Vol. 12 Issue 17, p2205-2212, 8p

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

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