Efficiency of numerical schemes for two dimensional Gray Scott model
نویسندگان
چکیده
منابع مشابه
Gray - Scott Model
In this paper, we rigorously prove the existence and stability of asymmetric spotty patterns for the Gray-Scott model in a bounded two dimensional domain. We show that given any two positive integers k 1 ; k 2 , there are asymmetric solutions with k 1 large spots (type A) and k 2 small spots (type B). We also give conditions for their location and calculate their heights. Most of these asymmetr...
متن کاملPattern formation in the one-dimensional Gray - Scott model
In this work, we analyse a pair of one-dimensional coupled reaction-diffusion equations known as the Gray–Scott model, in which self-replicating patterns have been observed. We focus on stationary and travelling patterns, and begin by deriving the asymptotic scaling of the parameters and variables necessary for the analysis of these patterns. Single-pulse and multipulse stationary waves are sho...
متن کاملThe Stability and Dynamics of Localized Spot Patterns in the Two-Dimensional Gray-Scott Model
The dynamics and stability of multi-spot patterns to the Gray-Scott (GS) reaction-diffusion model in a two-dimensional domain is studied in the singularly perturbed limit of small diffusivity ε of one of the two solution components. A hybrid asymptotic-numerical approach based on combining the method of matched asymptotic expansions with the detailed numerical study of certain eigenvalue proble...
متن کاملOn Two Dimensional Gray-scott Model: Existence of Single Pulse Solutions and Their Stability
Gray-Scott model has been studied extensively in recent years. However, most of the results are in one dimensional. In this paper, we study the 2-D Gray-Scott system. We rst construct two single pulse solutions and then we establish the stability and instability of such solutions in terms of the parameters involved.
متن کاملComparison of two integration schemes for a micropolar plasticity model
Micropolar plasticity provides the capability to carry out post-failure simulations of geo-structures due to microstructural considerations and embedded length scale in its formulation. An essential part of the numerical implementation of a micropolar plasticity model is the integration of the rate constitutive equations. Efficiency and robustness of the implementation hinge on the type of int...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: AIP Advances
سال: 2019
ISSN: 2158-3226
DOI: 10.1063/1.5095517