PATTERNS FORMATION OF 2D SWIFT-HOHENBERG EQUATION - Wijaya, Marcellino
Starting from the natural convection process that forms various patterns in nature. To observe the patterns formed in nature, one of the equations that can describe the pattern formation process from convection is the Swift-Hohenberg equation. The Swift-Hohenberg equation being considered includes cubic and quintic nonlinearities. Before observing the patterns formed, stability analysis is carried out for the 1D Swift-Hohenberg equation by drawing a bifurcation diagram. In conducting stability analysis, linearization is performed on the equation, and the equation is observed as a whole. When analyzing the 1D Swift-Hohenberg equation as a whole, the Fast Fourier Transform method, Pseudo Arc-Length continuation, and the 4th-order Runge-Kutta method are used. From the stability analysis of the 1D Swift-Hohenberg equation, the Swift-Hohenberg equation is then constructed into 2D to observe the patterns formed. The patterns are obtained by simulating the 2D Swift-Hohenberg equation. The simulation is carried out for the case where the parameter r > 0 and r < 0. For the case r > 0, variations in disturbances at several points are performed, including 1, 2, 3, 4, and 400 points. For disturbances at 1, 2, 3, and 4 points, the parameter r = 0.5 is chosen, while for disturbances at 400 points, the parameter values chosen are r = 0.01, 0.5, 2, and 5. For the case r < 0, disturbances at 400 points are applied, and parameter values chosen include r = ?0.01 and ?0.67. The resulting patterns from the simulation are observed to study the formed patterns.