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Topic: Variable transformations
Replies: 3   Last Post: Sep 8, 2013 2:52 AM

 Messages: [ Previous | Next ]
 Kevin J. McCann Posts: 147 Registered: 12/7/04
Re: Variable transformations
Posted: Jul 23, 2013 5:14 PM

Here is some code that I think I found, but may have written, a long
time ago.

First the Function. The key is the Nest, which takes care of the
derivatives.

Clear[COV, DEQ, \[Psi], x, z, f, n]
COV::usage =
"COV[DEQ,\[Psi],x,z,f] changes the independent variable in a \
differential equation from x to z where x=f[z]. \[Psi] is the \
dependent variable or
function we are solving for.";

COV[DEQ_, \[Psi]_, x_, z_,
f_] := (DEQ /. {D[\[Psi][x], {x, n_Integer}] :>
Nest[(D[#, z]/D[f, z]) &, \[Psi][z], n], \[Psi][x] :> \[Psi][z],
x :> f}
)

Here is an example of the usage:

de = -(\[HBar]^2/(2 m)) \!\(
\*SubscriptBox[\(\[PartialD]\), \({x, 2}\)]\(\[Psi][x]\)\) +
1/2 m \[Omega]^2 x^2 \[Psi][x] - e \[Psi][x]

COV[de, \[Psi], x, z, \[Alpha] z + \[Beta]]

Hope this helps,

Kevin

On 7/23/2013 4:43 AM, Nicholas Chisholm wrote:
> Say I have some differential equation in terms of the independent variable
>
> Thanks!
>

Date Subject Author
7/23/13 Nicholas Chisholm
7/23/13 Kevin J. McCann
7/29/13 Alexei Boulbitch
9/8/13 Youngjoo Chung