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

摘要

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 Shishkintype 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.