Computer models that accurately predict the dynamics of nanoscale self-organization are vital towards knowledge-based nanomanufacturing. Here we present a first principles computational model of laser induced self-organization of thin metallic films (thickness <= 30 nm) into nanoscale patterns which eventually evolve into ordered nanoparticles. The pattern formation is initiated by a thin film hydrodynamic instability and the ensuing length scales are related to the intrinsic materials properties such as surface tension and van der Waal's dispersion forces. We discuss a fully implicit, finite-difference method with adaptive time step and mesh size control for the solution of the nonlinear, fourth-order PDE governing the thin film dynamics. These simulations capture the changing morphology of the film due to the competition between surface tension and van der Waals forces. Simulation results are used to understand the nonlinear amplification of film height perturbations ∼ (KT/γ)1/2, where K, T and γ represent the Boltzmann constant, absolute temperature, and surface tension respectively, leading eventually to film rupture.