<DOC>
<DOCNO>
777
</DOCNO>
<TITLE>
a technique for rendering approximate solutions to
physical problems uniformly valid .
</TITLE>
<AUTHOR>
lighthill,m.j.
</AUTHOR>
<BIBLIO>
phil. mag. 40, 1949, 1179.
</BIBLIO>
<TEXT>
  a method is described for treating
some of the characteristically
non-linear problems of physics, in
particular those involving a non-linear
partial differential equation for
which an approximate linearization is
permissible everywhere except in a
limited region, such as the neighbourhood
of (5) a singular characteristic
of the approximate solution, or of
approximation is valueless .  the
method involves a transformation of
an independent variable, which is
determined progressively with successive
approximations to the solution ..
only one step being necessary if a
first approximation valid uniformly
be obtained .  the method is most
easily understood in its application
to simple first order ordinary
differential equations, which are
studied in detail in 2 and 3 as a
preparation for the extension to
more complicated problems in 4, 5
and 6 .  physically, the longest
section, 6, concerns the /spread/ of
a progressive wave at infinity,
an important and essentially non-linear
process .
</TEXT>
</DOC>
