Motion of Patterns Modeled by the Gray-Scott Autocatalysis System in One Dimension
Provides numerical approximations for pattern formation in autocatalysis, but the contribution is incremental as it applies existing methods to a specific problem.
The study numerically models self-replicating pulses in the Gray-Scott system using two numerical methods, demonstrating pulse occupation and domain coverage in one dimension.
Occupation of an interval by self-replicating initial pulses is studied numerically. Two different approximates in different categories are proposed for the numerical solutions of some initial-boundary value problems. The sinc differential quadrature combined with third-fourth order implicit Rosenbrock and exponential B-spline collocation methods are setup to obtain the numerical solutions of the mentioned problems. The numerical simulations containing occupation of single initial pulse, non or slow occupation model and covering the domain with two initial pulses are demonstrated by using both proposed methods.