Numeric simulation of hexogonal nanoscale structure arrays formation in anodic aluminium oxide

In this article self-organization of nanoscale porous structure arrays in anodic metal oxide is considered. The mathematical model of the chemical reaction at the metal-oxide and oxide-electrolyte interfases is described. A weakly nonlinear analysis near the instability threshold result in two dimensional Kuramoto–Sivashinsky equation. Solution of this equation provides the same regular hexagonal pore arrays that are observed in physical experiments. In this work two stage complex Rosenbrock scheme, developed by author, is applied for numeric simulation of this problem. High accuracy $O(\tau^4)$ and L1-stability along with low complexity of this method allow to use conventional PC to perform calculations.