Testing a new conservative method for solving the Cauchy problem for Hamiltonian systems on test problems

DOI10.1134/S0965542520090031zbMath1451.65226OpenAlexW3095623001MaRDI QIDQ2208497

P. A. Aleksandrov, G. G. Elenin

Publication date: 3 November 2020

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

Full work available at URL: https://doi.org/10.1134/s0965542520090031

zbMATH Keywords

Hamiltonian systemsenergy conservationRunge-Kutta methods

Mathematics Subject Classification ID

Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Numerical methods for Hamiltonian systems including symplectic integrators (65P10)

Uses Software

• MPFR
• GSL
• Matplotlib

Cites Work

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• Embedded symmetric nested implicit Runge-Kutta methods of Gauss and Lobatto types for solving stiff ordinary differential equations and Hamiltonian systems
• On the conservativeness of two-stage symmetric-symplectic Runge-Kutta methods and the Störmer-Verlet method
• Adaptive nested implicit Runge-Kutta formulas of Gauss type
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta methods
• On the conservativeness of a two-parameter family of three-stage symmetric-symplectic Runge-Kutta methods
• Solving Ordinary Differential Equations I
• A Method for Solving Algebraic Equations Using an Automatic Computer
• MPFR
• Automatic error control in the Gauss-type nested implicit Runge–Kutta formula of order 6
• Energy- and Quadratic Invariants--Preserving Integrators Based upon Gauss Collocation Formulae
• On conjugate symplecticity of B-series integrators
• Geometric Numerical Integration

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