I want to plot the expression formed from numerically calculated Poisson integrals (aka fundamental solutions of heat equation). I can only get numerical values. This question arises from my previous one.

ODE system. We extract the solutions.

```
s = NDSolve({u'(x) == -3 W(x) + x, W'(x) == u(x) - W(x)^3, u(0) == -1,
W(0) == 1}, {u, W}, {x, 0, 200})
G = First(u /. s)
g = First(W /. s)
```

They will serve as initial conditions in Poisson integrals.

Now we choose parameter, some x and t and integration limits.

```
(Epsilon) = 1/10
T = -1/2
X = 10
p1 = -200
p2 = 200
```

Now we consctruct the expression.

```
Q1 = 1/( 2 Sqrt(Pi *((T) + 1)*((Epsilon))^(2))) NIntegrate(
Exp(-(Abs(X - (Xi)))^2/(4*((T) +
1)*((Epsilon))^(2))) g((Xi)) G((Xi))
(-1/(2*((Epsilon))^2)), {(Xi), p1, p2})
Q2 = 1/( 2 Sqrt(Pi *((T) + 1)*((Epsilon))^(2))) NIntegrate(
Exp(-(Abs(X - (Xi)))^2/(4*((T) +
1)*((Epsilon))^(2))) g((Xi)), {(Xi), p1, p2})
q = (-2 ((Epsilon))^2 )*(Q1/Q2)
```

I need to plot and animate `q`

for any x and t intervals. By the code above I can only get numerical values.

Tried to get the tables of values and then animate it like this…

```
plots = Table(
Plot((1/( 2 Sqrt(Pi *((t) + 1)*((Epsilon))^(2))) NIntegrate(
Exp(-(Abs(x - (Xi)))^2/(4*((t) +
1)*((Epsilon))^(2))) g((Xi)) G((Xi)) (-1/(2*(
(Epsilon))^2)), {(Xi), p1, p2}))/(1/(
2 Sqrt(Pi *((t) + 1)*((Epsilon))^(2))) NIntegrate(
Exp(-(Abs(x - (Xi)))^2/(4*((t) +
1)*((Epsilon))^(2))) g((Xi)), {(Xi), p1, p2})), {x,
0, 2}, PlotRange -> {-10, 10}), {t, -2, 0, .25});
ListAnimate(plots)
```

But Mathematica is just running and I receive the error that one number “is too small to represent as a normalized machine number”.

I think it should be very simple but I am a newbie in Wolfram Mathematica so I’m sorry if the question is too trivial. Hope to get help.