
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! >

