Recent content by mcooper

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...

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

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...

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...

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...

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 =...

Please ignore this stupid question. Appologies.

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...

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...

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

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...

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

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

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...

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