IIMAS - FENOMEC
UNAM
Modified Equations for Variational Integrators
por Resumen:
Numerical
discretizations of differential equations are often studied
through their modified equation. This is a differential
equation, usually obtained as a power series in the step
size, with solutions that interpolate the discretization. It
is well-known that if a symplectic integrator is applied to
a Hamiltonian system, then its modified equation is again
Hamiltonian. In this talk we discuss this property from the
Lagrangian side. We present a technique to construct a
Lagrangian for the modified equation from the discrete
Lagrangian defining the variational integrator. This is
particularly interesting in the case of degenerate
Lagrangians, where the Legendre transform cannot be used to
switch between the Lagrangian and Hamiltonian formulations.
Informes: coloquiomym@gmail.com, o al 5622-3564.