Numerical simulations of reaction–diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines

Ersoy Hepson Ö., Yiğit G., Allahviranloo T.

Computational and Applied Mathematics, vol.40, no.4, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.1007/s40314-021-01524-4
  • Journal Name: Computational and Applied Mathematics
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Applied Science & Technology Source, Computer & Applied Sciences, zbMATH
  • Keywords: Reaction-diffusion systems, Pattern formations, Brusselator model, Gray-Scott model, Schnakenberg model, Quartic-trigonometric B-splines, TURING PATTERNS
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

© 2021, SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional.This article concerns with the numerical investigations of the reaction–diffusion systems (RDSs) arising in the study of pattern formation in biological and chemical systems with the employment of the quartic-trigonometric B-spline functions. The computationally numerical scheme uses collocation method which is established by a relatively new B-splines for the spatial discretizations and, for time integration Crank–Nicolson technique is adapted. Therefore, solutions of the RDSs are assembled by the wholly discretized space-time scheme. A matrix stability analysis is performed for the numerical scheme after linearization process. Experimental cases include Brusselator model, Gray–Scott model, Schnakenberg model as well as a linear problem in one-dimensional domain. Numerical solutions are compared to the existing studies. Spatial pattern formation is demonstrated by present computational algorithm.