  We present an algorithm to solve very large one-dimensional disordered and
interacting few-particle systems. Our approach exploits the localized nature of
the eigenfunctions in real space to achieve a linear scaling with the total
system size $L$. This allows us to solve for all eigenfunctions of
single-particle systems with different types of disorder up to one billion
sites. Based on this technology we collect very detailed histograms of
properties of eigenfunctions, such as the localization length or the
participation ratio as a function of their energy. These histograms reveal
surprisingly rich fine structures, whose origins we discuss. We also apply the
algorithm to single particle problems where not all eigenfunctions are
localized and show how this is diagnosed. Finally we extend the algorithm to
interacting two-particle problems in the presence of disorder and demonstrate
that our algorithm is well suited to analyze the effect of interactions on
wavefunctions.
