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Re: mixed partial derivatives

  • To: mathgroup at smc.vnet.net
  • Subject: [mg91270] Re: mixed partial derivatives
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 13 Aug 2008 04:38:15 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <g7rij3$i8v$1@smc.vnet.net>

Narasimham wrote:

> When mixed derivatives are not allowed, what is the fix? TIA
> 
> p=D[X[u,v],u]; q=D[X[u,v],v]; r =D[X[u,v],u,u]; s=D[X[u,v],u,v];
> t=D[X[u,v],v,v];
> GC[u_,v_] = (r t - s^2)/(1+p^2 + q^2)^2
> NDSolve[{GC[u,v]==  1, X[u, 0] == Cosh[u], Derivative[0,1][X][u, 0] ==
> 0,
>         X[-3, v] == X[3, v]},X[u,v], {u,0,3},{v,0,3}]

Is your question related to the following messages I got on my system or 
it is something completely different?

In[1]:=

p = D[X[u, v], u];
q = D[X[u, v], v];
r = D[X[u, v], u, u];
s = D[X[u, v], u, v];
t = D[X[u, v], v, v];

GC[u_, v_] = (r t - s^2)/(1 + p^2 + q^2)^2

NDSolve[
  {GC[u, v] == 1,
   X[u, 0] == Cosh[u],
   Derivative[0, 1][X][u, 0] == 0,
   X[-3, v] == X[3, v]}, X[u, v], {u, 0, 3}, {v, 0, 3}]

Out[3]=

   (1,1)      2    (0,2)        (2,0)
-X     [u, v]  + X     [u, v] X     [u, v]
------------------------------------------
          (0,1)      2    (1,0)      2 2
    (1 + X     [u, v]  + X     [u, v] )

During evaluation of In[1]:= NDSolve`FiniteDifferenceDerivative::ordred: 
There are insufficient points in dimension 1 to achieve the requested 
approximation order. Order will be reduced to 1.

During evaluation of In[1]:= NDSolve`FiniteDifferenceDerivative::conw: 
There are insufficient points in dimension 1 to generate consistent 
finite different weights.

Out[4]=

            (1,1)      2    (0,2)        (2,0)
          -X     [u, v]  + X     [u, v] X     [u, v]
NDSolve[{------------------------------------------ == 1,
                   (0,1)      2    (1,0)      2 2
             (1 + X     [u, v]  + X     [u, v] )

                         (0,1)
    X[u, 0] == Cosh[u], X     [u, 0] == 0, X[-3, v] == X[3, v]}, X[u, v],

   {u, 0, 3}, {v, 0, 3}]

Regards,
-- Jean-Marc


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