Recent content by Thorra

Hey, I know it's been a while, but could you explain in a bit more detail? Though Runge-Kutta also has a 2-step version, right? With order of accuracy $\mathcal O(h^2)$ Btw could you explain the difference between local and global truncation errors (LTE and GTE)? As I understand it, the LTE...

Sounds like multi-step methods are better. They take in account the previous points in the case one point happesn to be a bit off. What possible disadvantage? Maybe if the function changes rapidly at one point, then the multistep method goes off the track cause of the previous multi-points...

Quick question: Could you tell how to approximate to $\mathcal O(h^4)$? :) The same $v''(x)$ or whatever works.

On a different note: do you know the differences and advantages between one-step and multiple-step methods of Cauchy problem? And difference between closed schemes $\phi(t_i,h_i,\omega_i,\omega_{i+1})$ and open schemes $\phi(t_i,h_i,\omega_i)$ besides just the fact that the $\omega_{i+1}$ is...

Well I'm sure knowing this aS the base idea won't hurt me. Ah Aah

Okay, I'm in a bit of a pickle here. Got the exam on thursday and (surprise) I am utterly clueless. I cannot grasp a lot of concepts, but here's some I'd like to at least get an idea of: Factorization method. I only scrapped that it is a special case of Gauss' Exclusion method, that you take a...

But when I do the calculations then it's only close to the analytic results if I change it the way I did.. (Though there's still a strange offset when I go along x-axis with y being constant)

Well, the fictive nodes are only necessary at the bondaries (upper ones), so yeah, when the laplace equation steered into a boundary point, it transformed the $u_{i+1,j}$ and $u_{i,j+1}$ variables to specific $u_{i,M+1}$ and $ u_{N+1,j}$ fictive points, which have their own special formulas...

Hello again. I got some help with this since I last posted, but I ran into a problem later on (when calculating all the points on the models when N=M=4,6,8,..,16) which suggested the whole job was done with the 1st level of approximation. So could the programming method (yes, there was...

I have a question: what do I need to change in this process for it to have approximation with fictive nodes? Rather than non fictive nodes. (It's both the Neuman and Robin BCs approximated with I don't know what method.)

So $U\cdot(H+G)=$\begin{matrix}\left(-\frac{2}{h^2}-\frac{2}{g^2}\right)&\frac{1}{h^2}+\frac{1}{g^2}&0&0&0\\ \frac{1}{h^2}+\frac{1}{g^2}&\left(-\frac{2}{h^2}-\frac{2}{g^2}\right)&\frac{1}{h^2}+\frac{1}{g^2}&0&0\\...

Like this you mean? $u(x,y)=\frac{y}{(1+x^2)+y^2}$. That's just a minor typo if that's what you meant. So what should the matrix look like? Because I cannot for the life of me figure out how it works for real. The books are useless. I can only think of this old thing (sorry, sticking with the...

Hmm.. maybe adding the quadratic expression after the parenthesis. $\frac{\partial u(x,1)}{\partial y}+\frac{2u(x,1)}{(1+x)^2+1} = \frac{1}{(1+x)^2+1}$ That would explain why have separate brackets for it. :D Like this, then? $$-\frac{4y}{(4+y^2)^2}=\frac{u(1+h,y) - u(1-h,y)}{2h} + \mathcal...

is that bad? With my level of underswtanding I think only the simple boundary conditions match the analytic solution [u(x,0) and u(0,y)] Which 2nd equation do you mean? Do you mean like this? $$-\frac{4y}{4+y^2)^2}=\frac{u(1+h) - u(1-h)}{2h} + \mathcal O(h^2)$$ sorry if I'm shooting really...

Nope, I rechecked and it is written that way. I know, weird, but maybe it's some implication from where it came from or whatever. Ha, I wish I could say that. I have 8 points on there and I want at least 4 done by monday so I can hope for a passing grade. Still stuck at 2! Ooooh! Well that...