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Symplecticity and Quadratic Invariants
Aleksandr Ayvazov
UCSD
Abstract:
In this talk, we explore the relationship between Symplecticity and the preservation of quadratic invariants. Symplectic Runge-Kutta methods, the bread and butter of numerical geometric integration, are exactly the ones that preserve all quadratic first integrals of a system. But when we expand our focus to larger classes of methods, we will find a more nuanced connection. It is also known that for symplectic RK methods, the action of discretization commutes with forming variational equations, and we will discuss the expansion of this result to a larger class of methods.
Tuesday, April 11, 2017
11:00AM AP&M 2402
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Randolph E. Bank
Philip E. Gill
Michael Holst
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Randolph E. Bank
Philip E. Gill
Michael Holst
Administrative Contact:
[ Click to Send Email ]
Aleksandr Ayvazov
UCSD
Abstract:
In this talk, we explore the relationship between Symplecticity and the preservation of quadratic invariants. Symplectic Runge-Kutta methods, the bread and butter of numerical geometric integration, are exactly the ones that preserve all quadratic first integrals of a system. But when we expand our focus to larger classes of methods, we will find a more nuanced connection. It is also known that for symplectic RK methods, the action of discretization commutes with forming variational equations, and we will discuss the expansion of this result to a larger class of methods.
Tuesday, April 11, 2017
11:00AM AP&M 2402