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

DOI10.1134/S0965542515030100zbMath1325.65105MaRDI QIDQ498584

G. Yu. Kulikov

Publication date: 29 September 2015

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

numerical examplesstiff systems\(A\)-stabilityHamiltonian equationsembedded formulasstiff initial value problemsymplecticityautomatic error controlnested implicit Runge-Kutta methodRunge-Kutta methods of Gauss and Lobatto typesvariable-stepsize mesh generation

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15) Numerical methods for stiff equations (65L04)

Related Items (9)

Accurate cubature and extended Kalman filtering methods for estimating continuous-time nonlinear stochastic systems with discrete measurements ⋮ How to avoid accuracy and order reduction in Runge-Kutta methods as applied to stiff problems ⋮ Estimating the domain of absolute stability of a numerical scheme based on the method of solution continuation with respect to a parameter for solving stiff initial value problems ⋮ Nested implicit Runge-Kutta pairs of Gauss and Lobatto types with local and global error controls for stiff ordinary differential equations ⋮ Testing a new conservative method for solving the Cauchy problem for Hamiltonian systems on test problems ⋮ Practical implementation of extended Kalman filtering in chemical systems with sparse measurements ⋮ NIRK-based Cholesky-factorized square-root accurate continuous-discrete unscented Kalman filters for state estimation in nonlinear continuous-time stochastic models with discrete measurements ⋮ Implicit Runge-Kutta methods with explicit internal stages ⋮ Estimating the State in Stiff Continuous-Time Stochastic Systems within Extended Kalman Filtering

Uses Software

• Matlab
• RKC
• RODAS

Cites Work

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