This book addresses the task of computation from the standpoint of asymptotic analysis and
multiple scales that may be inherent in the system dynamics being studied. This is in contrast
to the usual methods of numerical analysis and computation. The technical literature is replete
with numerical methods such as Runge-Kutta approach and its variations finite element methods
and so on. However not much attention has been given to asymptotic methods for computation
although such approaches have been widely applied with great success in the analysis of dynamic
systems. The presence of different scales in a dynamic phenomenon enable us to make judicious
use of them in developing computational approaches which are highly efficient. Many such
applications have been developed in such areas as astrodynamics fluid mechanics and so on.
This book presents a novel approach to make use of the different time constants inherent in the
system to develop rapid computational methods. First the fundamental notions of asymptotic
analysis are presented with classical examples. Next the novel systematic and rigorous
approaches of system decomposition and reduced order models are presented. Next the technique
of multiple scales is discussed. Finally application to rapid computation of several aerospace
systems is discussed demonstrating the high efficiency of such methods.
