<DOC>
<DOCNO>
479
</DOCNO>
<TITLE>
on an equation occurring in falkner and skan's approximate
treatment of the equation of the boundary layer .
</TITLE>
<AUTHOR>
hartree,d.r.
</AUTHOR>
<BIBLIO>
proc. cam. phil. s. 33, 1937, 223.
</BIBLIO>
<TEXT>
  the differential analyser
has been used to evaluate solutions of the equation y''' = -yy'' +
with boundary conditions y = y' = 0 at x = 0, as
which occurs in falkner and skan's approximate treatment of the
laminar boundary layer (see abstract 1081 (1932)) .  a numerical
iterative method has been used to improve the accuracy of the solutions,
and the results show that the accuracy of the machine solutions is about
insufficient to specify a unique solution for negative values of,.
a discussion of this situation is given, and it is shown that for the
application to be made of the solution the appropriate condition is that
from below, and as rapidly as possible, as .  the condition that
from below can be satisfied only for values of greater than a limiting
value whose value is approximately -0.199, and which is related to the
point at which the laminar boundary layer breaks away from the
boundary .
</TEXT>
</DOC>
