Numerical scheme for solving the nonuniformly forced cubic and quintic Swift-Hohenberg equations strictly respecting the Lyapunov functional

Abstract

Computational modeling of pattern formation in nonequilibrium systems is a fundamental tool for studying complex phenomena in biology, chemistry, materials science and engineering. The pursuit for theoretical descriptions of some among those physical problems led to the Swift-Hohenberg equation (SH3) which describes pattern selection in the vicinity of instabilities. A finite differences scheme, known as Stabilizing