G-symplectic second derivative general linear methods for Hamiltonian problems

DOI10.1016/j.cam.2016.10.011zbMath1353.65133OpenAlexW2532593599MaRDI QIDQ344310

Mohammad Hasan, M. Dambrine

Publication date: 22 November 2016

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2016.10.011

zbMATH Keywords

numerical experimentsgeneral linear methodsparasitismG-symplecticityHamiltonian problemssecond derivative methodslong-time integration

Mathematics Subject Classification ID

Numerical methods for Hamiltonian systems including symplectic integrators (65P10) Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems (37M15)

Related Items (11)

Efficient Nordsieck second derivative general linear methods: construction and implementation ⋮ Composite symmetric second derivative general linear methods for Hamiltonian systems ⋮ Symmetric second derivative integration methods ⋮ Algebraic stability and irreducibility of second derivative methods ⋮ Implementation of second derivative general linear methods ⋮ Implicit-explicit second derivative diagonally implicit multistage integration methods ⋮ Order conditions for second derivative general linear methods ⋮ General linear methods with projection ⋮ Projection of second derivative methods for ordinary differential equations with invariants ⋮ Partitioned second derivative methods for separable Hamiltonian problems ⋮ Numerical conservation laws of time fractional diffusion PDEs

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Numerical integration of Hamiltonian problems by G-symplectic methods
• An extension of general linear methods
• Maximal order for second derivative general linear methods with Runge-Kutta stability
• On explicit two-derivative Runge-Kutta methods
• The cohesiveness of G-symplectic methods
• Order conditions for G-symplectic methods
• The existence of symplectic general linear methods
• Runge-Kutta schemes for Hamiltonian systems
• Canonical Runge-Kutta methods
• Implementation of Nordsieck second derivative methods for stiff ODEs
• G-symplecticity implies conjugate-symplecticity of the underlying one-step method
• On the construction of second derivative diagonally implicit multistage integration methods for ODEs
• Two-derivative Runge-Kutta methods for PDEs using a novel discretization approach
• New second derivative multistep methods for stiff systems
• Energy conservation with non-symplectic methods: examples and counter-examples
• Second derivative methods with RK stability
• Explicit Canonical Methods for Hamiltonian Systems
• The Order of Numerical Methods for Ordinary Differential Equations
• Dealing with Parasitic Behaviour in G-Symplectic Integrators
• The Control of Parasitism in $G$-symplectic Methods
• Geometric Numerical Integration
• Second Derivative Multistep Methods for Stiff Ordinary Differential Equations

This page was built for publication: G-symplectic second derivative general linear methods for Hamiltonian problems