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02/26/12 08:46am

Hi there. Just wanted to make a 3d plot of the 1-d heat equation. Very new to Mathematica so a little green. This was all given

(ut is partial wrt time, etc...)

ut - 0.1uxx = f(x,t)

u(0,t) = v (initial conditions)
u(x,2) = g1 (boundary conditions)
u(x,3) = g2

We are given u(x,t) = [sin(4x) + cos(2x)] [cos(t) + sin(t)]

And now Mathematica input

u[x, t] = (sin[4*x] + cos[2*x])*(cos[t] + sin[t])
dt = D[u[x, t], t]
dxx = D[u[x, t], {x, 2}]

v = (sin[4*x] + cos[2*x])*(cos[t] + sin[t])/.t->0
g1 = (sin[4*x] + cos[2*x])*(cos[t] + sin[t])/.x->2
g2 = (sin[4*x] + cos[2*x])*(cos[t] + sin[t])/.x->3
f = dt - 0.1*dxx

Then using NDSolve

pde = NDSolve[{D[u[x, t], {t, 1}] == 0.1*D[u[x, t], {x, 2}] + f,
u[x, 0] == v, u[2, t] == g1, u[3, t] == g2},
u, {x, 2, 3}, {t, 0, 2}]

NDSolve::ndnum: Encountered non-numerical value for a derivative at t == 0

Can't get away from this. Any help would be greatly appreciated.

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Author Date Posted
Encountered non-numerical Value, For Heat Eqn Autobot 02/26/12 08:46am
Re: Encountered non-numerical Value, For Heat Eqn jf 02/26/12 7:02pm
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