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Do much.

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We just need to plot and see how the solution changes with time.

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We already plot the first solution.

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Let's.

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Let's plot it again so we have it here.

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A plot it here and shift enter we can see at.

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Well, basically time equals well, the first time step, it equals zero.

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And as we know, the shape of you, you shape.

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You or let's say length of you is that time it we have 100,000 time steps.

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So what we need to do is we simply take this.

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Of course, there are more sophisticated way to show the answer to actually make a simulation, but

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I want to keep things as simple as possible.

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And what we care about to this is already the X and we just need to change the time step.

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So the first 500 steps we can see this is what we started.

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And then after 500 steps of time, we have this much, let's say after 1000 steps we can see more diffusion

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happening after.

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10,000 steps.

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We can see more diffusion happening towards the center.

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After 50,000 step, now it looks like a quite beautiful start from 100 and then it will go all the way

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to ten.

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And.

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After.

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A like basically the last one 100,000 steps.

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We cannot have 100.

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So we need nine, 9999 and we remove this one.

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So.

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Hundred thousand.

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We need to just.

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Divide like minus one one unit because we as we said the temperature that in Python from zero to the

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length.

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So we can see the diffusion happening this way.

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So we start from 100 and we get to the last one, which is 200.

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Just one thing I didn't mention.

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I would say in this thing we didn't update the boundary condition, so this is why we didn't update

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it.

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We put from one, we start the counting from one.

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If we count from zero, we will have a problem because or we will basically the boundary condition will

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change and it will be a problem because the boundary condition, um, will you need the t need to start

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from initial condition.

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So we cannot here but let's say here, sorry, the X, if we put it zero here, it will be zero minus

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one.

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It will have minus one.

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There is nothing minus before the this point so it will cause us trouble.

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And of course.

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It's physically wrong.

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So this is why we put it starting from one and we the length minus one.

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The reason is also the same thing.

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What we will do is we will not calculate the last point.

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We should not calculate the last point.

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And actually this is, of course, that we don't have a point of 100,000 or like in the X, we will

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not have the point of 100.

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But.

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In this the range thing.

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The final point, he will not he will exclude it.

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It it will not it will like if it's from 0 to 100, it will start from zero until 99.

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This is what's going to happen.

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If we put here 100, 100, they will not calculate it.

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So this is what this is why these boundary condition didn't affected by this update.

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Now, it might be confusing, but please do it yourself and I hope you already coded with with me what

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we can see.

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It's always a problem to deal with the boundary condition.

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And this one point here, one point there, it might cause a trouble.

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So this is why I emphasized it now, because I didn't emphasize this point before.

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Anyway, this way how we solve the well, our heat equation one, the heat equation using our code from

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from zero and next, let's see other equations how we can solve it.

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We go from 1D, we have to go to 2D and then in the numerical of course methods and later we will continue

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to the actual solving these equations using neural networks.