Numerical Simulation Technique for Nonlinear Singularly Perturbed Predator-Prey Reaction Diffusion System in Biomathematics

In biomathematics, singularly perturbed predator-prey systems are of common occurrence. A singularly perturbed problem with nonlinear predator-prey reaction diffusion system in 2 dimension is studied. The system changes rapidly near initial time layer. Traditional numerical method failed to simulate...

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Bibliographic Details
Main Authors: Xin Cai, Zhong-di Cen
Format: Conference Proceeding
Language:English
Subjects:
Biological system modeling
Computational modeling
Delay systems
Equations
Fluid dynamics
Mathematics
Numerical simulation
Predator prey systems
Production
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Summary:In biomathematics, singularly perturbed predator-prey systems are of common occurrence. A singularly perturbed problem with nonlinear predator-prey reaction diffusion system in 2 dimension is studied. The system changes rapidly near initial time layer. Traditional numerical method failed to simulate the system. Numerical simulation of this kind of system is rare so far, this motives us to consider novel simulation technique. Firstly stretched variable is introduced so that the analytic solution is decomposed into the reduced solution and the initial layer correction solution. Secondly, the nonlinearization process of the reduced problem system is proposed. Thirdly, two numerical method, stretched variable method and Shishkin- type method, are constructed. Finally, simulation example is studied to demonstrate that both stretched variable method and Shishkin-type method are efficient computational method. Shishkin-type method is more practical in use for this kind of complicated system.
ISSN:2157-9555
DOI:10.1109/ICNC.2007.507