proceedings

FO RUM PRO C E E DIN G S
g(x) is a function of one variable only. The equation is
linear and of the second order. Now a more general equation
of the second order in the normal forn) may be
written
d 2
S = g(xJ S) S + p(x)
dx 2
This equation is non-linear. You might conceivably treat
it in the same manner as the speaker has suggested, except
that you would obviously run into the difficulty of .computing
the quanties Yn. We might construct some sUltable
program beforehand and use it to estimate the Yn. I wonder
if either of you gentlemen have tried such a method. .
Dr. Thomas: This is exactly the thing that Hartree dId
in his so-called "Self-consistent Field" computations.
There are two ways you can do it. vVith the notation:
where
He used V and any numerical approximation to t/ln to get
V nJ then solved the differential equation to get t/lnJ these to
get new V and VnJ and so on until you come out with
what you put in. A somewhat different trick was one we
tried a few years ago. Instead of assuming Vn we assumed
V and put o/n to get Vn continuously as t/ln was being computed.
I don't think you gain anything by that, except that
every answer you get is a solution of the differential
equation.
Dr. Caldwell: It might be possible to do that kind of
thing with the 602 provided the functions were not too
complicated.
Dr. Thomas: It was the double integral that I had in
mind. You can do two of them simultaneously on the
405 as well as the constant. You go all through an
integration to get preliminary values for t/ln. These must
be normalized. These integrals must be obtained to get an
"energy" to put in on the right-hand side before repeating
the integration.
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