Numerical analysis of Bazykin–Berezovskaya model

Zafar Z. U. A., Tauseef Saeed S., Rehan Qureshi M., Tunç C.

Journal of Taibah University for Science, vol.17, no.1, 2023 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 17 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1080/16583655.2023.2190020
  • Journal Name: Journal of Taibah University for Science
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Keywords: Bazykin-Berezovskaya (BB) model, backward Euler method, CN method, equilibrium points, NSFD method, stability analysis
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

In this manuscript, a Bazykin–Berezovskaya model with diffusion by strong Allee effects is studied. Neumann boundary conditions are used to see the positive solution of a diffusion system. Local stability analyses are discussed for all the equilibrium points. The analysis of stability for the proposed scheme is also given. Implicit finite difference schemes like: Euler, Crank–Nicolson (CN) and non-standard finite difference (NSFD) are used to verify the simulation by numerically. A comparison reveals that NSFD method is unconditionally stable for any temporal step-size.