Quite a lot of effort goes into refining numerical methods. The optimization of your codes are without any doubt far inferior to what is already implemented by matlab. Also being able to learn the standard way to implement is a very crucial skill itself.
>integral(@(x)x./(exp(x)-1),0,1)
This is how you integrate in Matlab. It is ridiculous to implement your own algorithm for anything other than educational purposes.
I am no expert but you can look into "2D absorbing boundary conditions."
I got that part correct, right? You have a Z polarized E field, xy polarized H field traveling in xy plane?
http://www.engr.uky.edu/~gedney/courses/ee624/notes/EE624_Notes6.pdf
I have implemented this in 1D, you need to...
I actually solved this qustion after much work, however I do not like m solution. It would be great if someone could link me somewhere that derives error function laplace transforms
Those symbols don't mean anything to me, so I do not know which one is the input.
Even so, I can say that it is non linear because there is nothing in that expression for which there could be a linear relationship.
It would be a good idea to actually understand what "linearity" means whether it...
e^{kx} cannot be a solution but I decided to try e^{k(x)} which gave me a ricatti equation and after I substituted k=q\frac{p'}{p} I got the original equation
edit: this is the solution
c_1e^{\frac{-x^2}{4}+x}+c_2e^{\frac{-x^2}{4}+x} \int ^x e^{\frac{-s^2}{2}+2s}ds
I know y=e^{t-t^2/2} is a solution but how do I reach it? I tried substituting y=uv, making u' terms disappear then I noticed that the resulting u''=(__)u could be solved by a gaussian but this seems like luck to me
It basically boils down to:
show that:
$$\int_{-\infty}^{\infty} dy \frac{J_1 \left ( \pi\sqrt{x^2+y^2} \right )}{\sqrt{x^2+y^2}} = \frac{2 \sin{\pi x}}{\pi x} $$
My life story (somewhat irrelevant):
A jinc function is besselj(1,pi*r)/( 2r ), a sinc is sin(pi*x) / (pi*x)
I have noticed, while...
I want to understand how water waves behave. I do not need to be able to solve them (although i would like a derivation) because I tried hard to find it but I were not able to find any source on it (i probably didn't know the terms i should have been searching for)
The type of stuff I want to...