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Okay the question is:

"Compute numerical approximations to the above IVP on the interval $[t_0,te]=[0,1]$. Use step sizes of $h = 0.1, 0.01, 0.001$ and display in a table the results $y_j$ and the errors $e_j = y(x_j ) − y_j$ for all three methods* at the 11 locations $x_k =0, 0.1, 0.2, . . . , 0.9, 1.0.$ You can also plot the functions. (this is voluntarily)"

The IVP is:

$y'(x)=-2xy(x)^2, y(0)=y_0=1$

For $h=0.1$ the computation was easy to do. But when I let $h=0.01$ is it true that I should make a table of 100 steps? And how about $h=0.001$? Should I also do a table with 1000 steps? I hope I misunderstand the question here.

If I'm wrong here. How should I do it then? I mean how should I make a table where $h=0.01$ and $h=0.001$.

*Btw the three methods my teacher mentioned is "Euler", "Heun" and "Midpoint".

Lutz Lehmann
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NabbKitha
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1 Answers1

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If you read carefully the task that you copied, it says

"display in a table the results $y_j$ and the errors $e_j = y(x_j ) − y_j$ for all three methods* at the 11 locations $x_k =0, 0.1, 0.2, . . . , 0.9, 1.0.$"

so that for $h=0.01$ you display the values for $j=10k$ and for $h=0.001$ for $j=100k$.

For inspiration on how to structure the code for such a task see https://math.stackexchange.com/a/1239002/115115

Lutz Lehmann
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  • So let me understand this correct. I should compute all 100 steps, but only show j=10k, i.e. j=3, that is 10*3=30 so the 30th step, and so on. Got it?

    In other words. Step 0, Step 10, Step 20, Step 30, ... Step 100.

    Must be shown?

     – NabbKitha Sep 30 '18 at 11:28
  • Yes, exactly that. I did something similar in https://math.stackexchange.com/a/1239002/115115 – Lutz Lehmann Sep 30 '18 at 14:27
  • You are my man! – NabbKitha Sep 30 '18 at 19:09