I have three functions dependent on three independent variables, like so:
H[u,m,s] S[u,m,s] SH[u,m,s]
However, I don't actually know these functions--they are solutions to three partial differential equations much like this (very simplified) example:
DEQ1 = u*D[H[u,m,s],u]-12*S[u,m,s]+1/4*SH[u,m,s]==0; DEQ2 = u*D[S[u,m,s],u]-2*S[u,m,s]+6*SH[u,m,s]==0; DEQ3 = u*D[SH[u,m,s],u]+3*S[u,m,s]+4*SH[u,m,s]==0;
I want to impose the following conditions:
H[u,m,s] > 0 0 < S[u,m,s] < 4*Pi -4*Pi < SH[u,m,s] < 4*Pi
and plot the allowed parameter space that satisfies all of these conditions ('s' as a function of 'm', for a specified range of 'u'). How would I do this? I have absolutely no idea. I need to do a 'scan' of a parameter space and plot the points (the functions are such that I can only solve numerically), but I don't know how to do this. Any insight would be much appreciated.