Understanding Non-Linear PDEs: Causes and Implications

  • Thread starter Thread starter robousy
  • Start date Start date
  • Tags Tags
    Non-linear
robousy
Messages
332
Reaction score
1
What makes a PDE non-linear please?

Thanks!
 
Physics news on Phys.org
Do you know what makes an ordinary diff. eq. non-linear?
 
Do you know what nonlinear means? :)
 
Having a non-linear function of the dependent function anywhere in the equation. I suspect arildno and Tide were wondering how you could be studying partial differential equations if you don't know what "non-linear" means!
 
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...

Similar threads

Back
Top