Re: Partial Differential Equation

*To*: mathgroup at smc.vnet.net*Subject*: [mg26676] Re: Partial Differential Equation*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Wed, 17 Jan 2001 00:47:27 -0500 (EST)*Organization*: Universitaet Leipzig*References*: <93r7gq$4q4@smc.vnet.net>*Sender*: owner-wri-mathgroup at wolfram.com

Hi, Mathematica can't solve nonlinear boundary value problems. Regards Jens "P. Poinas" wrote: > > 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