Solution of u_tt+(1/3)u_rrrr-u_rr-(1/5)u_t=0, where u is the wave surface height and r is the radial coordinate. The solution is found analytically in time and using Fourier Series in space. The code was written in Matlab.
Sure thing...I don't remember where I hid the code on my computer, but here is a link to spectral solver example I gave my class:
people.clarkson.edu/~barlowns/MA331/spectral.m
It is set with the Fourier coefficients a,b, and c for the convective-diffusion equation. For the "puddle equation" (really just a generic 4th order dispersive wave equation), use
@gianniacampora
Sure thing...I don't remember where I hid the code on my computer, but here is a link to spectral solver example I gave my class:
people.clarkson.edu/~barlowns/MA331/spectral.m
It is set with the Fourier coefficients a,b, and c for the convective-diffusion equation. For the "puddle equation" (really just a generic 4th order dispersive wave equation), use
a=1; b=-1/5; c=1/3*k.^4+k.^2; %puddle
instead. have fun!
barlowns 9 months ago