Symplectic Euler method
In numerical mathematics , the symplectic Euler method is a modification of the Euler method for solving Hamilton's equations , certain systems of ordinary differential equations that occur in classical mechanics . It has the same effort as the Euler method, but still delivers better results. The symplectic Euler method can be viewed as a combination of the explicit and the implicit Euler method .
In general, a numerical calculation method is called symplectic if it describes a symplectic mapping when applied to a Hamilton system. Symplectic methods maintain the symplectic structure . This is desirable because the flow of Hamilton systems is symplectic and, because of their symplecticity, the methods also receive certain conservation quantities of the flow.
Individual evidence
- ↑ Marlis Hochbruck : With mathematics to reliable simulations: numerical methods for solving time-dependent problems . In: Katrin Wendland , Annette Werner (Hrsg.): Multifaceted Mathematics: Insights into modern mathematical research for everyone who wants to understand more about mathematics . Vieweg + Teubner, Wiesbaden 2011, ISBN 978-3-8348-1414-2 , pp. 191–214 , here p. 196 .
- ↑ Michael Griebel , Stephan Knapek, Gerhard Zumbusch , Attila Caglar: Numerical simulation in molecular dynamics: numerics, algorithms, parallelization, applications . Springer, Berlin 2004, ISBN 978-3-540-41856-6 , here pp. 224-225 .