TY - JOUR
T1 - An efficient and accurate numerical scheme for turing instability on a predatorprey model
AU - Yun, Ana
AU - Jeong, Darae
AU - Kim, Junseok
N1 - Funding Information:
This work was supported by National Junior research fellowship from the National Research Foundation of Korea grant funded by the Korea government (No. 2011-0012258). The authors also wish to thank the reviewers for the constructive and helpful comments on the revision of this article.
PY - 2012/6
Y1 - 2012/6
N2 - 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.
AB - 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.
KW - Turing instability
KW - ratio-dependent predatorprey
KW - semi-implicit scheme
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U2 - 10.1142/S0218127412501398
DO - 10.1142/S0218127412501398
M3 - Article
AN - SCOPUS:84863840815
VL - 22
JO - International Journal of Bifurcation and Chaos
JF - International Journal of Bifurcation and Chaos
SN - 0218-1274
IS - 6
M1 - 1250139
ER -