Subject: Change of variable for differential equation
From: Daniel Lakeland
Date: Sun, 17 Jun 2007 11:44:23 -0700
Suppose I have a differential equation such as
deq: diff(h(x),x) = g(x);
I want to express solutions in terms of a nondimensional variable t
where x depends on t via an affine transformation.
xeqn: x = a*t-b;
how can I most easily accomplish the transformation of this
differential equation into an equation in terms of t? Preferrably I
would like to accomplish this in an automated way rather than a lot of
by-hand substitutions (the actual equations might be significantly
more complicated)
It obviously doesn't work to simply say subst(xeqn,deq) because I wind
up with something like this:
d
(%o3) -------- (h(a t - b)) = g(a t - b)
da t - b
Is there a way to convert that funky differential operator to an
application of the chain rule? how about for higher derivatives?
--
Daniel Lakeland
dlakelan at street-artists.org
http://www.street-artists.org/~dlakelan