Recent content by mcooper

  1. M

    Understanding L2-Norm & Equation: Error Analysis Help

    Hi, thanks for your reply. I am in need of something that will give me a "global" error of an solution that I have. I have a plot of the approximation against the exact value and I am guessing I need to calculate the area between the 2 curves (hence the equation in the 1st post?). Can the L2...
  2. M

    Understanding L2-Norm & Equation: Error Analysis Help

    What is the difference between this equation and the sum of the errors squared?
  3. M

    Understanding L2-Norm & Equation: Error Analysis Help

    Could someone please explain to me in fairly basic terms what the L2-norm is and what it does please. More specifically let me know what the following equation does, if possible... E(N) = 2*pi \int (U(N) - Uexact)2 r dr Where E is the error for a specific N. Ultimately I have values for an...
  4. M

    Understanding the L2-Norm and its Equation

    Could someone please explain to me in fairly basic terms what the L2-norm is and what it does please. More specifically let me know what the following equation does... E(N) = 2*pi\int(u(N) - uexact)2 r dr Where E is the error for a specific N. I haven't found any good resources for...
  5. M

    Simpson's Rule in Matlab

    Oh yes thanks. I was wondering, with this method would it be possible to have the numbers of singularities on the inner and outer ring different? I am guessing a problem would arise when calculating the weights as the multiplying matrix is not square so may not have an inverse...
  6. M

    Simpson's Rule in Matlab

    A quick question with regards to plotting the results. I am trying to plot the results for various N in a 2D graph but am struggling slightly. I tried this for the last few lines of the code but it doesn't seem to be quite right and wondered of you could have a look... Phiann =...
  7. M

    Simpson's Rule in Matlab

    Please ignore this stupid question. Appologies.
  8. M

    Simpson's Rule in Matlab

    I've had a chance to look through it and understand pretty much all of it, it looks great. One part I don't quite understand is why there are 'minus' signs in front of an integral over the inner boundary. I think it's to do with the orientation of the innner integral but can't think why it...
  9. M

    Simpson's Rule in Matlab

    The 2 fundamental solutions are \psi = logrj and \psiin = logrinj. I have not derived these solutions myself but have just lifted them from papers. By the superpostion principle the sum of fundamental solutions of a linear PDE is also a solution. Again, I have attached a short pdf and I...
  10. M

    Simpson's Rule in Matlab

    Note: for now I have taken N=M i.e. there are the same number of singularities on the inner and outer rings.
  11. M

    Simpson's Rule in Matlab

    My aim is to adapt the method to work for annular domains. Like before I have a ring of singularities outside of the domain but now I have also a ring of singularities on the inside of the domain. I have attached a short outline of the problem (I find it easier to typeset). Here is the...
  12. M

    Can 7 divide 3^(2n+1) + 2^(n+2) in induction for number theory?

    The inductive hypothesis is that 7 divides 3^(2k+1) + 2^(k+2)
  13. M

    Can 7 divide 3^(2n+1) + 2^(n+2) in induction for number theory?

    Homework Statement Show 7 divides 3^(2n+1) + 2^(n+2) The Attempt at a Solution Have proved base case K=1 and for the case k+1 I have got ot the point of trying to show 7 divides 9.3^(2k+1) + 2.2^(k+2). Any pointers would be much appreciated. Thanks in advance
  14. M

    Finding Last Digits of 3400: Without Calculator or Euler's Totient Function

    Sorry that's poor, its been a long day/night. All powers of 5 are congruent to 625 mod 1000 (hence 25 mod 100). Kind of weird but kind of cool. Is there a mathematical reason/proof for this? mod 10000 they are not all the same...
  15. M

    Finding Last Digits of 3400: Without Calculator or Euler's Totient Function

    Are the powers of 5 easy because (5,1000)=1 so you can use Euler's Theorem?
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