ndsolve pde+ode problem
- To: mathgroup at smc.vnet.net
- Subject: [mg85006] ndsolve pde+ode problem
- From: marian.ostrowski at gmail.com
- Date: Tue, 22 Jan 2008 02:00:43 -0500 (EST)
Dear Colleagues,
I have encountered a problem with the NDSolve solver with solving
simple wave equation (PDE) with the ordinary diff equation on the
boundary (ODE). My intention is to model bar/string structure type
with attached mass (with initial velocity) on the end, while second
end is fixed. Because modeling of the PDE+ODE seems to be impossible,
I have tried to model the ODE as PDE, by simply adding a second
variable x. Below I have attached this piece of code I tried to use.
s = NDSolve[{ (*impact mass-bar problem*)
(*PDE*)
Derivative[2, 0][u][x, t] == Derivative[0, 2][u][x, t],
(Derivative[0, 2][g][x, t]) == (Derivative[1, 0][u][x, t] /.x ->
0),(*force equilibrium - coupling condition*)
(*IC*)
u[x, 0] == 0,(*initial displacement field*)
g[x, 0] == 0,
(Derivative[0, 1][u][x, t] /. t -> 0) ==0,(*initial velocity
field*)
(Derivative[0, 1][g][x, t] /. t -> 0) == 1,
(*BC*)
(u[x, t] /. x -> 0) == (g[x, t] /.x -> 0),(*displacement
equilibrium- coupling condition*)
(u[x, t] /. x -> 1) == 0 (*no displacement at the end*)
},
{u, g}, {t, 0, 10}, {x, 0, 1}]
And the Mathematica says: "NDSolve::ndincb: Initial conditions are not
of consistent \
dimensionality."
Can you try to help me?
Best regards,
Marian