### CAS Seminar

# Mats Vermeeren

### (TU Berlin)

## "Modified equations for variational integrators"

** Date: ** |
Wed, November 18, 2015 |

** Time: ** |
11:15 |

** Place: ** |
Research I Seminar Room |

**Abstract:** Numerical integration of Lagrangian (variational) ODEs is often done by discretizing the variational principle rather than the differential equations themselves. Numerical integrators obtained this way are called variational integrators and they exhibit very good long-time behavior. This can be explained using backward error analysis: one looks for a modified differential equation that interpolates the numerical solution. It turns out that this modified equation is a Lagrangian ODE as well. In my talk I will present a construction of a modified Lagrange function that generates the modified equation. Although the final result could easily be obtained from the theory of symplectic integrators for Hamiltonian ODEs, the details of the construction are surprisingly different from the Hamiltonian case.