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.

**Truth tables?**

**Re: L'Hopital's rule contradiction --- what am I messing up?**

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

**Trying to use Solve - temp1a.nb (0/1)**