       Partial Differential Equation

• To: mathgroup at smc.vnet.net
• Subject: [mg26623] Partial Differential Equation
• From: "P. Poinas" <ppoinas at estec.esa.nl>
• Date: Sat, 13 Jan 2001 22:36:05 -0500 (EST)
• Organization: European Space Technology and Research Centre (ESTEC)
• Sender: owner-wri-mathgroup at wolfram.com

```Dear Group,

I am trying to solve the following problem:

\!\(\(\(NDSolve[{\(T''\)[R] + \((1/\((R + 0.05)\))\)\ \(T'\)[R] -
10\^\(-8\)\ \ T[R]\^4 == 0, \(T'\) == \(-0.07\), \
\(T'\) ==
0}, \ T, \ {R, \ 0, \ 1}]\)\(\ \)\)\)

and I get the following message:

NDSolve::"inrhs": "Differential equation does not evaluate to a number
or the \
equation is not an nth order linear ordinary differential equation."

I know that this error is because I am defining the derivative at 2
different R values:

at R=0, T'[0 ]= -0.07
and R=1, T' = 0

hence it is not an initial boundary condition.

1) How can I turn around the problem?

Actually, I found the Mathematica Book (V4) very weak on the subject. In
page 924, it seems possible in In to find a solution to a linear
differential equation, even with 2 boundary conditions defined at 2
different x values! My problem being not linear cannot therefore be
solved. But Mathematica does not mentioned the linearity as a show
stopper.

2) Does anybody know a better description of Mathematica's capacity?

Thank you for helping me,

Philippe Poinas

```

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