Andrei
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 Jun 20 comment Adaptive sampling for slow to compute functions in 2D Well, a robust algorithm for 2D adaptive sampling would be very nice to have. Jun 20 comment Adaptive sampling for slow to compute functions in 2D Are there any new developments on this issue? Jul 11 comment Complex valued 2+1D nonlinear PDE using NDSolve @ruebenko, could you please clarify one thing? in your answer, are the boundary conditions assumed to be periodic or not? because in the documentation, for the "pseudospactral" difference order, it looks like that! I am asking because I wanted mine to be fixed.. Jul 11 comment solve ODE with divergencies @ThiesHeidecke, since you seem to know a lot about numerical methods for solving differential equations, could you please recommend a good book on the topic? Jul 11 comment solve ODE with divergencies @ThiesHeidecke, excellent, thanks a lot for the effort! Jul 9 comment solve ODE with divergencies great! @ThiesHeidecke, could you please detail on the Hankel/Bessel approaches? Jul 9 comment Complex valued 2+1D nonlinear PDE using NDSolve i did in the original post, but somehow it got lost in the editing :) well nevermind that, the real problem indeed are the boundaries, because it seems like there is reflection there, and I need to simulate the system as if it were infinite Jul 9 comment Complex valued 2+1D nonlinear PDE using NDSolve About the boundary conditions, what I can say based on physical arguments is that far away from the center (at infinity), the solution tends to 1. Jul 9 comment Complex valued 2+1D nonlinear PDE using NDSolve Trying you code, NDSolve chokes with the error "Maximum number of 10000 steps reached at the point t == 1.92". Also, could you please edit your answer to plot Abs[sol]^2 instead of the imaginary part please? That is the physical quantity of interest ;) Jul 9 comment Complex valued 2+1D nonlinear PDE using NDSolve The "pseudospectral" difference order, from what I understand from the docs, applies FFT methods, which basically assumes periodic boundary conditions, right? Whereas mine were fixed (Dirichlet type). Jul 9 comment solve ODE with divergencies I also don't understand why your solution has a negative slope at the end of the interval, when it should flatten out towards $f$=1 at $\eta=10$. Jul 8 comment solve ODE with divergencies $s$ is not a parameter, it is in fact the quantum number corresponding to the z component of the angular momentum, therefore it can only have values 1,2,3,.. and I am particularly interested in the case $s=1$. Jun 14 comment Digital filter of image in Fourier space @AndrewJaffe simply because I don't know how to do it in practice :)) Jun 14 comment Digital filter of image in Fourier space In case of confusion: I am in fact only interested in the last image (the one corresponding to the raw data). Jun 14 comment Digital filter of image in Fourier space nice! is there any way to do the reverse, i.e. a kind of low-pass filter that gets rid of these small waves? Jun 14 comment Digital filter of image in Fourier space @nikie, the FFT in my question corresponds to the image just above it, which is for a homogeneous system. The problem I am interested in, which is the last image of my question, being inhomogeneous will of course have a more complicated FFT, but one can still see circles (using exponential scale). Jun 14 comment Digital filter of image in Fourier space @nikie, i uploaded a better image and the raw data corresponding to it is now on Pastebin. Jun 13 comment Digital filter of image in Fourier space in fact, i would like to upload the raw data, but its a large matrix and i'm not sure how to do that Jun 13 comment Digital filter of image in Fourier space great work @nikie. one thing remains - isn't there some way of selecting just the waves which correspond to a certain ring in the Fourier transformed image? say something like a band pass filter which selects one ring? because i know that the close-spaced waves on the left of the center correspond to one particular ring only (namely the bright ring on the left of the 2D fft plot). May 19 comment Overloading conjugate operator for a particular function Ok @gpap, I followed your advice, hope you don't mind! :)