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
>
>
>
>

```

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