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...
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 =...
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...
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...
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...