Do much.
We just need to plot and see how the solution changes with time.
We already plot the first solution.
Let's.
Let's plot it again so we have it here.
A plot it here and shift enter we can see at.
Well, basically time equals well, the first time step, it equals zero.
And as we know, the shape of you, you shape.
You or let's say length of you is that time it we have 100,000 time steps.
So what we need to do is we simply take this.
Of course, there are more sophisticated way to show the answer to actually make a simulation, but
I want to keep things as simple as possible.
And what we care about to this is already the X and we just need to change the time step.
So the first 500 steps we can see this is what we started.
And then after 500 steps of time, we have this much, let's say after 1000 steps we can see more diffusion
happening after.
10,000 steps.
We can see more diffusion happening towards the center.
After 50,000 step, now it looks like a quite beautiful start from 100 and then it will go all the way
to ten.
And.
After.
A like basically the last one 100,000 steps.
We cannot have 100.
So we need nine, 9999 and we remove this one.
So.
Hundred thousand.
We need to just.
Divide like minus one one unit because we as we said the temperature that in Python from zero to the
length.
So we can see the diffusion happening this way.
So we start from 100 and we get to the last one, which is 200.
Just one thing I didn't mention.
I would say in this thing we didn't update the boundary condition, so this is why we didn't update
it.
We put from one, we start the counting from one.
If we count from zero, we will have a problem because or we will basically the boundary condition will
change and it will be a problem because the boundary condition, um, will you need the t need to start
from initial condition.
So we cannot here but let's say here, sorry, the X, if we put it zero here, it will be zero minus
one.
It will have minus one.
There is nothing minus before the this point so it will cause us trouble.
And of course.
It's physically wrong.
So this is why we put it starting from one and we the length minus one.
The reason is also the same thing.
What we will do is we will not calculate the last point.
We should not calculate the last point.
And actually this is, of course, that we don't have a point of 100,000 or like in the X, we will
not have the point of 100.
But.
In this the range thing.
The final point, he will not he will exclude it.
It it will not it will like if it's from 0 to 100, it will start from zero until 99.
This is what's going to happen.
If we put here 100, 100, they will not calculate it.
So this is what this is why these boundary condition didn't affected by this update.
Now, it might be confusing, but please do it yourself and I hope you already coded with with me what
we can see.
It's always a problem to deal with the boundary condition.
And this one point here, one point there, it might cause a trouble.
So this is why I emphasized it now, because I didn't emphasize this point before.
Anyway, this way how we solve the well, our heat equation one, the heat equation using our code from
from zero and next, let's see other equations how we can solve it.
We go from 1D, we have to go to 2D and then in the numerical of course methods and later we will continue
to the actual solving these equations using neural networks.