G-symplecticity implies conjugate-symplecticity of the underlying one-step method

DOI10.1007/s10543-013-0437-1zbMath1282.65168OpenAlexW2041581726MaRDI QIDQ2434941

Raffaele D'Ambrosio, Ernst Hairer, C. J. Zbinden

Publication date: 3 February 2014

Published in: BIT (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10543-013-0437-1

zbMATH Keywords

general linear methodunderlying one-step methodconjugate-symplecticG-symplecticmulti-value method

Mathematics Subject Classification ID

Nonlinear ordinary differential equations and systems (34A34) Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (14)

Solving nonlinear parabolic PDEs in several dimensions: parallelized ESERK codes ⋮ G-symplectic second derivative general linear methods for Hamiltonian problems ⋮ Partitioned general linear methods for separable Hamiltonian problems ⋮ Underlying one-step methods and nonautonomous stability of general linear methods ⋮ An iterative starting method to control parasitism for the Leapfrog method ⋮ Multivalue collocation methods free from order reduction ⋮ Long-term stability of multi-value methods for ordinary differential equations ⋮ General linear methods with projection ⋮ G-symplectic integration of many body problems ⋮ General Nyström methods in Nordsieck form: error analysis ⋮ Nearly conservative multivalue methods with extended bounded parasitism ⋮ Partitioned second derivative methods for separable Hamiltonian problems ⋮ Multi-value Numerical Methods for Hamiltonian Systems ⋮ A symmetric nearly preserving general linear method for Hamiltonian problems

Cites Work

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• Long-term stability of multi-value methods for ordinary differential equations
• The existence of symplectic general linear methods
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• On conjugate symplecticity of B-series integrators
• Dealing with Parasitic Behaviour in G-Symplectic Integrators
• The Control of Parasitism in $G$-symplectic Methods
• Geometric Numerical Integration
• Conservation of integrals and symplectic structure in the integration of differential equations by multistep methods
• Numerical Methods for Ordinary Differential Equations

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