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From: TrinhDao on 17 Jul 2010 08:15
Dear Mathematica users,

I want to transform one different equation (variable r,z) to another
different equation (variable x,y).

The origin equation is :
equation = Derivative[0, 2][u][r, z] + Derivative[1, 0][u][r, z]/r +
Derivative[2, 0][u][r, z] == 0

The transform rule is :

r = Cos[x]Sinh[y]
z = Sin[x] Cosh[y]

============

Now, my task is simple, apply this transform to differential equation.
I do like this :

transformRule = {r[x][y]-> Cos[x]Sinh[y], z[x][y]-> Sin[x] Cosh[y]}
dtrules=Join @@ ({#,D[#,t],D[#,{t,2}]} & /@ transformRule)

But it seems that something is wrong...

=========

And the analytical result is :

anaSolution = 1 / (Sin^2[x] + Sinh^2[y] ) * ( Derivative[2, 0][u][x,y]
+ -Tan[x]*Derivative[1, 0][u][x, y] + Derivative[0, 2][u][x, y] +
Tanh[y]*Derivative[0, 1][u][x, y] )


==========

Can someone do this ? It seems simple but infact, when i touch it, it
made the complex result. So what i want is how to obtain the
anaSolution.

Waiting for ur help...


From: janos on 19 Jul 2010 02:09
On j=FAl. 17, 14:15, TrinhDao <hackerdarkr...(a)yahoo.com> wrote:
> Dear Mathematica users,
>
> I want to transform one different equation (variable r,z) to another
> different equation (variable x,y).
>
> The origin equation is :
> equation = Derivative[0, 2][u][r, z] + Derivative[1, 0][u][r, z]/r +
> Derivative[2, 0][u][r, z] == 0
>
> The transform rule is :
>
> r = Cos[x]Sinh[y]
> z = Sin[x] Cosh[y]
>
> ============
>
> Now, my task is simple, apply this transform to differential equation.
> I do like this :
>
> transformRule = {r[x][y]-> Cos[x]Sinh[y], z[x][y]-> Sin[x] Cosh[y]}
> dtrules=Join @@ ({#,D[#,t],D[#,{t,2}]} & /@ transformRule)
>
> But it seems that something is wrong...
>
> =========
>
> And the analytical result is :
>
> anaSolution = 1 / (Sin^2[x] + Sinh^2[y] ) * ( Derivative[2, 0][u][x,y]
> + -Tan[x]*Derivative[1, 0][u][x, y] + Derivative[0, 2][u][x, y] =
+
> Tanh[y]*Derivative[0, 1][u][x, y] )
>
> ==========
>
> Can someone do this ? It seems simple but infact, when i touch it, it
> made the complex result. So what i want is how to obtain the
> anaSolution.
>
> Waiting for ur help...

This might help, try it.

http://library.wolfram.com/infocenter/MathSource/4186/

J=E1nos

From: thaihang le on 20 Jul 2010 03:42
Thanks and rated for you Janos

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