Wave simulations of Gray-Scott reaction-diffusion system

TOK ONARCAN A., ADAR N., DAĞ İ.

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, vol.42, no.16, pp.5566-5581, 2019 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 16
  • Publication Date: 2019
  • Doi Number: 10.1002/mma.5534
  • Journal Name: MATHEMATICAL METHODS IN THE APPLIED SCIENCES
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.5566-5581
  • Keywords: collocation, Gray-Scott model, reaction-diffusion systems, trigonometric quartic B-spline, PATTERN-FORMATION, OSCILLATIONS
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this work, we study the numerical simulation of the one-dimensional reaction-diffusion system known as the Gray-Scott model. This model is responsible for the spatial pattern formation, which we often meet in nature as the result of some chemical reactions. We have used the trigonometric quartic B-spline (T4B) functions for space discretization with the Crank-Nicolson method for time integration to integrate the nonlinear reaction-diffusion equation into a system of algebraic equations. The solutions of the Gray-Scott model are presented with different wave simulations. Test problems are chosen from the literature to illustrate the stationary waves, pulse-splitting waves, and self-replicating waves.