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] == \(-0.07\), \
\(T'\)[1] ==
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'[1] = 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[7] 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