Structure-preserving numerical integration or ordinary and partial differential equations

Applied and Computational Mathematics Seminar
Monday, December 1, 2014 - 2:00pm
1 hour (actually 50 minutes)
Skiles 005
GA Tech
It is the
purpose of this talk to analyze the behaviour of multi-value numerical
methods acting as structure-preserving integrators for the numerical
solution of ordinary and partial differential equations (PDEs), with
special emphasys to Hamiltonian problems and reaction-diffusion PDEs. As
regards Hamiltonian problems, we provide a rigorous long-term error
analyis obtained by means of backward error analysis arguments, leading
to sharp estimates for the parasitic solution components and for the
error in the Hamiltonian. As regards PDEs, we consider
structure-preservation properties in the numerical solution of
oscillatory problems based on reaction-diffusion equations, typically
modelling oscillatory biological systems, whose solutions oscillate both
in space and in time. Special purpose numerical methods able to
accurately retain the oscillatory behaviour are presented.