An efficient and accurate numerical scheme for turing instability on a predatorprey model

Ana Yun, Darae Jeong, Junseok Kim

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present an efficient and accurate numerical method for solving a ratio-dependent predatorprey model with a Turing instability. The system is discretized by a finite difference method with a semi-implicit scheme which allows much larger time step sizes than those required by a standard explicit scheme. A proof is given for the positivity and boundedness of the numerical solutions depending only on the temporal, but not on the spatial step sizes. Finally, we perform numerical experiments demonstrating the robustness and accuracy of the numerical solution for the Turing instability. In particular, we show that the numerical nonconstant stationary solutions exist.

Original languageEnglish
Article number1250139
JournalInternational Journal of Bifurcation and Chaos
Volume22
Issue number6
DOIs
Publication statusPublished - 2012 Jun

Keywords

  • Turing instability
  • ratio-dependent predatorprey
  • semi-implicit scheme

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering (miscellaneous)
  • General
  • Applied Mathematics

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