I have been thinking about this, would I have to define:
<br />
C=\frac{\partial}{\partial x}\int Cdx<br />
and then define
<br />
B'=B-\int Cdx<br />
to get
<br />
\frac{\partial A}{\partial t}+\frac{\partial B'}{\partial x}=0<br />
and then apply Lax-Wendroff to the above equation?
There is the following linear Volterra equation of the second kind
$$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$
with kernel
$$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$
where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
Are there any good visualization tutorials, written or video, that show graphically how separation of variables works?
I particularly have the time-independent Schrodinger Equation in mind. There are hundreds of demonstrations out there which essentially distill to copies of one another. However I am trying to visualize in my mind how this process looks graphically - for example plotting t on one axis and x on the other for f(x,t).
I have seen other good visual representations of...