You are invited to attend the Masters Thesis Defense of Hari Datt Pandey
in the Department of Mathematics & Statistics.

Thesis Defense:  Thursday, July 26, 2012 (1pm-2:30pm) AB 109

Hari Datt Pandey
Department of Mathematics and Statistics
University of Nevada, Reno
Numerical Computations on Normal Forms of Nonlinear Systems

Abstract:  Poincare's normal forms method became a prevailing approach
to qualitative analysis of local bifurcation phenomena undergoing in
nonlinear dynamical systems.  However its numerical accuracy frequently
depreciated in extended neighborhoods of a core solution due to poor
convergence/divergence of the underlying successive approximations.  This
limits the practical value of this method.  In the past decades substantial
efforts were devoted to improve convergence of normalizing approximations
which result in the celebrated KAM M-theory.  This work develops
a numerical approach to deriving the normal forms and corresponding
nonlinear change of variables which eliminates poorly convergent/divergent
successive approximations.  We adopt the function-al structure of the
normal forms method but determine the corresponding coefficients by
minimizing the least square error of system solutions which are emanated
from a given neighborhood of a core solution.  We show on a few examples
that this approach provides a higher precision than the standard
technique.