Multistep methods integrating ordinary differential equations on manifolds. (English) Zbl 0996.65073
The authors show how a reformulation of multistep methods in a Lie group setting can preserve the configuration space of the underlying problem. This approach also holds in the more general setting of general linear methods. Some numerical comparisons are made between backward differentiation formula methods, Adams-Moulton methods and Runge-Kutta methods.
Reviewer: Kevin Burrage (Brisbane)
MSC:
| 65L05 | Numerical methods for initial value problems involving ordinary differential equations |
| 65L06 | Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations |
| 34A34 | Nonlinear ordinary differential equations and systems |
Keywords:
multistep methods; Lie group setting; linear methods; numerical comparisons; backward differentiation formula; Adams-Moulton methods; Runge-Kutta methodsSoftware:
DiffManReferences:
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