Numerical integration of Hamiltonian problems by G-symplectic methods. (English) Zbl 1301.65127
The authors introduce and analyze a general linear method in order to solve Hamiltonian problems. Their method is one of order 4, symmetric and G-symplectic, with bounded parasitic components. It requires a lower computational effort than the symplectic Runge-Kutta methods at the same accuracy level. Some numerical experiments are carried out in order to confirm the qualities of the method.
Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
Keywords:
Hamiltonian problems; geometric numerical integration; general linear methods; B-series method; symmetric methods; G-symplectic methods; comparison of methods; symplectic Runge-Kutta methods; numerical experimentsReferences:
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