Although the Partial Differential Equations (PDE) models that
are now studied are usually beyond traditional mathematical
analysis, the numerical methods that are being developed and used
require testing and validation. This is often done with PDEs that
have known, exact, analytical solutions. The development of
analytical solutions is also an active area of research, with many
advances being reported recently, particularly traveling wave
solutions for nonlinear evolutionary PDEs. Thus, the current
development of analytical solutions directly supports the
development of numerical methods by providing a spectrum of test
problems that can be used to evaluate numerical methods.
This book surveys some of these new developments in analytical
and numerical methods, and relates the two through a series of PDE
examples. The PDEs that have been selected are largely "named''
since they carry the names of their original contributors. These
names usually signify that the PDEs are widely recognized and used
in many application areas. The authors intention is to provide a
set of numerical and analytical methods based on the concept of a
traveling wave, with a central feature of conversion of the PDEs to
ODEs.
The Matlab and Maple software will be available for download
from this website shortly.
www.pdecomp.net
Includes a spectrum of applications in science, engineering,
applied mathematicsPresents a combination of numerical and
analytical methodsProvides transportable computer codes in Matlab
and Maple"
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