I have a question from my book and it says essentially, consider the IVP with , what is the exact value of , then using Eulers method with step size1 , estimate call this , then repeat for step sizes of for then finally plot as a function of step size and then as vs .
Now I am having some issues and ill explain,
for the first part I get that
We have and
so I have that by Euler method
which would imply that for
and then for the second part it would imply , then 0.99, then 0.999 and finally 0.9999.
But this doesn't seem to make any sense to me. Seeing as none of these are close to
So I am confused in regard to where I am making mistakes, or where everything is going wrong. For the plotting part, I am also stuck because of this. I am looking for any help and advice.