# IVP differential equation with Euler Method

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".

## 1 Answer

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

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