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, ***** your input **** 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 ***** and, without further adoo : 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