Formal series and numerical integrators. I: Systems of ODEs and symplectic integrators. (English) Zbl 0929.65126
An investigation of the order conditions of numerical methods for systems of differential equations (DEs) and differential-algebraic equations (DAEs) is presented. More specifically a new approach for the production and handling of the series expansions in which lead the order conditions for systems of DEs and DAEs is presented. In this paper the investigation of one-step methods is presented. The approach is applied to the investigation of NB-series methods to which the well-known Runge-Kutta methods belong. An investigation of numerical integration of Hamiltonian systems by symplectic integrators is also presented.
Reviewer: T.E.Simos (Xanthi)
MSC:
| 65P10 | Numerical methods for Hamiltonian systems including symplectic integrators |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 37M15 | Discretization methods and integrators (symplectic, variational, geometric, etc.) for dynamical systems |
| 65L80 | Numerical methods for differential-algebraic equations |
Keywords:
symplectic integrators; one-step methods; Runge-Kutta methods; NB-Series; Hamiltonian systems; order conditions; differential-algebraic equationsSoftware:
RODASReferences:
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