@m_goldberg What exactly do you mean by that? (sry kind of new and interessted)

If I could I would hug you right now. I have been struggeling with this for the better part of the last 3 weeks! Thanks!

@MMM Yeah unfortunatly it is. I don't want to plot it, that was different question (Thanks again for that, btw ;)), but I would like to use the values, in my function for ongoing calculations. Ultimately I would like to define a function as fw[x] (as stated above) which I can use as a boundary value lateron.

@MMM I'm sry I'm an idiot. I tried to simplify my problem but just made it worse. So now I posted the original try. As a little sidenote: The e-Functions are there so I don't the inconsistent boundary conditions error. The singular point at the beginning unfortunatly is problem related. Thanks for the help so far though. I can see you are really trying

@MMM Sry misread your comment xD... added it

Same example only 2D sol1 = NDSolve[{ D[f1[x, \[Xi]], \[Xi]] == g1[x, \[Xi]], D[g1[x, \[Xi]], \[Xi]] == h1[x, \[Xi]], D[h1[x, \[Xi]], \[Xi]] + f1[x, \[Xi]]*h1[x, \[Xi]] == 0, f1[x, 0] == 0, g1[x, 0] == 1, g1[x, 10] == 0, f1[0, \[Xi]] == 0, g1[0, \[Xi]] == 0, h1[0, \[Xi]] == 0 }, {f1, g1, h1}, {x, 0, 1}, {\[Xi], 0, 10}] Plot[D[g1[x, \[Xi]], \[Xi]] /. sol1, {\[Xi], 0, 10}, PlotRange -> All] Plot[h1[x, \[Xi]] /. sol1, {\[Xi], 0, 10}, PlotRange -> All]

f[x,0] is part of the previewious calculation. An interpolating function from NDsolve, sry forgot to mention