Recent content by Romik

Hey there, I have modeled a propagating wave in a 1D dispersive media, in which square and cubic nonlinear terms are present. u′′=au3+bu2+cu the propagating pulse starts to steepen with time which is the effect of nonlinearity, but there is an effect which I can't understand. so...

Thanks Chester for your reply. yes, that means zero displacement at both ends. finite difference (FD) is the first approach that came in mind and I searched over internet to find similar PDEs with FD, and all I found was linear wave PDE (same as your link), or nonlinear first order...

Hi guys, I need to simulate wave propagation for a nonlinear dispersive wave PDE and since I can't find proper resources for handling nonlinear PDEs numerically, I would appreciate any help and clues. the PDE is in the form of utt-(au+bu2+cu3+duxx)xx=0 Romik Ps: BC: Clamped at both ends IC...

Hi all, I have a simple question about 3D plotting. Consider this simple loop, which provides y and O for any x. and I am able to plot y vs O for given x. for Omega=0:.01:5 y(i)=(x*Omega^2); O(i)=Omega; i=i+1; end now consider I want to change the value of x, for x=0:.1:3...

Thank you so much for your time and help. Unfortunately I need a relation (even approximation) explicitly and I can't go with numerical solution, I tried Mathematica before, I know, it doesn't help. I'm thinking about Jacobi elliptic function, or generalized Riccati equation method...

Thanks again for the comment, These types of equations are called "Autonomous" and they are very common in classical mechanics (Hamiltonian systems) in this case $$\frac{d^2u}{dx^2}=f(u)$$ is second order special case! (it is independent of first order derivative). terms in $$f(u)$$ come...

You are right, Thanks.

Yes, obviously the DE is that expression. Thanks for comment

Hi guys, Here is an equation that I have tried for few days to solve and still haven't succeeded, I'm interested to solve this 4th order wave equation to find u(x). ∫∫(A u(x) + B u(x)2 + C u(x)3 +D u''(x)) dx dx=0 the 4th term is second derivative of displacement u(x). I assume...

thanks mfb for you helpful comments. can you explain more about Newton method, how could I apply it on my equation? I use Mathematica! with Series function, I am able to truncate my original polynomial to 4th degree, now how should I apply Newton since I don't have numerical root and my...

Thanks for the reply, biggest or smallest positive root, that's not the main issue here, I need to find an approximate root based on variables, reduce from 6th degree to let's say 4th degree which I can solve it exactly.

Hi all, I have been stopped by a sextic (6th degree) polynomial in my research. I need to find the biggest positive root for this polynomial symbolically, and since its impassible in general, I came up with this idea, maybe there is a way to approximate this polynomial by a lower degree...