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    Could somebody please have a look at my graph and tell me whether it is ok to demonstrate convergence? As in is everything clear etc?

    Thanks in advance!
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    according to the maths mod sitting next to me...she has no idea
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    I don't think it's possible to comment without a lot more context. As it stands (without the context), I wouldn't be pleased with it as an examiner, because it doesn't actually give enough information to know what's going on. (What's N, what's M, etc.)
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    Thank you for the reply, and sorry - stupid of me not to realise context would be needed. I have attached the relevant rabulated data in this post.

    I'm basically using the Gauss quadrature rule, to approximate the integral for x^1/2.

    For this I have used a number of points, n, within the rule as 1, 2 and 5. M is the number of sections the interval is split up into, i.e:

     I_{a,b}^M = \sum_{j=1}^M I_{(a + (j-1)h, a + jh)}[f]

    However there are two things I'm unsure about.

    Firstly for N = 2 and 5, only 5 and 1 approximations respectively are needed to get to 6.d.p of the exact solution. So for these I have only plotted those points, however would it be preferable to show further approximations, even if they are all on the exact solution line?

    And secondly I'm unsure whether using a loglog graph is the right approach, this is what we have been advised to use but would a semi-log graph not be better?
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    I don't know for certain, but I think y-axis should be "log(approximation error)" not log(approximation). I'd just put M on the x-axis as well (not log M)
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    Thank you so much David, that makes a lot more sense.
 
 
 
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Updated: February 4, 2010

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