       Re: NDSolve: X D[f[X,Z],X] - D[f[X,Z],Z,Z] == 0

• To: mathgroup at smc.vnet.net
• Subject: [mg8331] Re: [mg8196] NDSolve: X D[f[X,Z],X] - D[f[X,Z],Z,Z] == 0
• From: seanross at worldnet.att.net
• Date: Sun, 24 Aug 1997 13:24:47 -0400
• Sender: owner-wri-mathgroup at wolfram.com

```> > Michael Bunk wrote:
> > >
> > > I have tried to solve the problem:
> > >
> > >         X D[f[X,Z],X] - D[f[X,Z],Z,Z] == 0
> > > with
> > >         f[X,0] == 0
> > >         Derivative[0,1][f][X,1] == 0,
> > >         f[1,Z] == Sin[Z Pi/2]
> > >
> > >         f,{X,1,5},{Z,0,1}
> > >
> > > but MATHEMATICA 3.0 says:
> > >
> > >         The right-hand side of the differential equation does not evaluate to a
> > > number at X==1.
> > >
> > > What's wrong with my formulation?

sean ross wrote:
> > What is the point of the zero on the right hand side of your equality?
> > Try it again but having one partial equaling another instead of the
> > difference equaling zero.  This may not fix the problem, but I doubt the
> > problem is with the zero.  You need to try other formulations to figure
> > out exactly what mathematicas objection is.

Michael Bunk wrote:
> The same equation with Z instead of X in the first term :
>
>         Z D[f[X,Z],X] - ....
>
> works very well. I think it's a problem of this X but i try....
>
> To deal with the zero on the right-hand-side is impossilbe, because it's
> the physics of my problem.
>
sean ross wrote:

What I meant was, write

X D[f[X,Z],X] - D[f[X,Z],Z,Z] == 0

as

X D[f[X,Z],X] == D[f[X,Z],Z,Z]

and see what happens.  This doesn't change the physics of the
problem,but may give you a better idea about what mathematicas problem
is.  Intrinsic to many numerical methods is that the way you write the
equation determines the outcome.  For example, if I want to solve the
equation x^2 = Exp[x] and want to use fixed point iteration to do so,
writing

x[[n+1]]=Sqrt[Exp[x[[n]]]] may yield a different root than if I write

x[[n+1]]=2 Log[x[[n]]], though both are algebraically equivalent.

```

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