Re: 4th order DE, NDSolve no solution, why?

*To*: mathgroup at smc.vnet.net*Subject*: [mg15690] Re: [mg15686] 4th order DE, NDSolve no solution, why?*From*: "Kevin J. McCann" <kevinmccann at home.com>*Date*: Mon, 1 Feb 1999 14:54:11 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Doug, NDSolve doesn't do two-point boundary value problems. All the BC's must be given at a single point. To solve your problem, you need to try a shooting technique or else something like a finite-difference or finite-element approach. Kevin -----Original Message----- From: Doug Webb <D_Webb at prodigy.net> To: mathgroup at smc.vnet.net Subject: [mg15690] [mg15686] 4th order DE, NDSolve no solution, why? >Hello, > I'm trying to solve a 4th order diferential equation with NDSolve, and >I get the following error, anyone know why? The equation is that for >buckling of a column: > >GoverningEqn = modulus*inertia*w''''[x] + P[x]*w''[x] == 0 > >with lower order equations to support it like so: > >Theta[x_] := -w'[x] >M[x_] := -modulus*inertia*w''[x] >V[x_] := -P[x]*w'[x] - modulus*inertia*w'''[x] > >where w[x] is the deflection, Theta[x] is the rotation, M[x] is the >moment, and V[x] is the shear. I define the applied load P[x] as a >simple constant in this case: > >P[x_] := 1 > >modulus and inertia are also defined as constants for this first simple >case: > >inertia = 5 >modulus = 100 > >and make for simplicity this time, a column that is Pi units long: L = >Pi > >Now, using the boundary conditions for a pinned-pinned column of w[0] = >w[L] = M[0] = M[L] = 0, I try to solve using the following command: > >soln = NDSolve[ {GoverningEqn, w[0] == 0, w[L] == 0, M[0] == 0, M[L] == >0}, > w, {x, 0, L} ] > >I get the following errors: > >NDSolve::"unsol": > "Not possible to initiate boundary value problem with the chasing >method" >NDSolve::"unsol": > "Not possible to initiate boundary value problem with the chasing >method" > >Why? What other method can I use? Everything I try with >Method->"something" gives the same result, Runge-Kutta, Gear, etc. >Anyone have any idea why I can't get a solution? DSolve runs, but >returns an empty rule for the solution: {} > >Please, anyone that knows what I'm doing wrong, let me know. Thanks! > > Doug > D_Webb at prodigy.net > > > >