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