Re: Changing PDE to ODE

• To: mathgroup at smc.vnet.net
• Subject: [mg7524] Re: [mg7509] Changing PDE to ODE
• From: "w.meeussen" <w.meeussen.vdmcc at vandemoortele.be>
• Date: Tue, 10 Jun 1997 23:17:59 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

```hi Sergio,

In[32]:=eq1 = a^2*u[0][x, y, z] +
Derivative[2, 0, 0][u[0]][x, y, z] == 0

Out[32]=
2                       (2,0,0)
a  u[0][x, y, z] + (u[0])       [x, y, z] == 0

In[33]:=eq2 = b^2*Derivative[0,1,0][u[1]][x,y,z] +
Derivative[0,2,0][u[1]][x,y,z]==0

Out[33]=
2       (0,1,0)                  (0,2,0)
b  (u[1])       [x, y, z] + (u[1])       [x, y, z] == 0

***** definitions : *****

In[34]:=u[0][x,y,z]:=u[0][y];
Derivative[n_,0,0][u[0]][x,y,z]:=Derivative[n][u[0]][x]
In[36]:=u[1][x,y,z]:=u[1][y];
Derivative[0,n_,0][u[1]][x,y,z]:=Derivative[n][u[1]][y]

***** end definitions *****

In[38]:=eq1
Out[38]=
2
a  u[0][y] + (u[0])''[x] == 0

In[39]:=eq2
Out[39]=
2
b  (u[1])'[y] + (u[1])''[y] == 0

It's what's in The Book under "LaplaceTransform", discussing "Heat
Conduction PDE".

greetings,

At 03:48 7-06-97 -0400, Sergio Rojas wrote:
> Hello guys,
>
>   	I have a set of PDE that may be solved using ODE techniques.
>	In general, they look (after using FullForm) like :
>
>eq1 = a^2*u[0][x, y, z] + Derivative[2, 0, 0][u[0]][x, y, z] == 0
>
>eq2 = b^2*Derivative[0,1,0][u[1]][x,y,z] + Derivative[0,2,0][u[1]][x,y,z]==0
>
>  	By using Mathematica, how these equations can be
>	transformed into ordinary differential equation
>        that may looks like:
>
>a^2*u[0][x] + Derivative[2][u[0]][x] == 0
>
>b^2*Derivative[1][u[1]][y] + Derivative[2][u[1]][y] == 0
>
> 	One can take care of the Derivative by using:
>
>neweq2 = eq2 /. Derivative[0, n_, 0] -> Derivative[n]
>
>	How to change [x,y,z] to [y] ?
>
>Sergio
>
>E-mail: sergio at scisun.sci.ccny.cuny.edu
>
>
>
>
>

Dr. Wouter L. J. MEEUSSEN
eu000949 at pophost.eunet.be
w.meeussen.vdmcc at vandemoortele.be

```

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