4th order DE, NDSolve no solution, why?

• To: mathgroup at smc.vnet.net
• Subject: [mg15686] 4th order DE, NDSolve no solution, why?
• From: "Doug Webb" <D_Webb at prodigy.net>
• Date: Sun, 31 Jan 1999 03:06:08 -0500 (EST)
• Organization: Prodigy Services, Inc
• Sender: owner-wri-mathgroup at wolfram.com

```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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