Positive and elementary stable nonstandard numerical methods with applications to predator-prey models. (English) Zbl 1087.65068

The authors introduce and analyze a class of methods for the numerical solution of predator-prey equations. The methods are constructed in a way that retains some important analytical properties of the systems. Numerical computations indicate the superiority over standard methods that do not follow these construction criteria at least for certain important situations.


65L05 Numerical methods for initial value problems involving ordinary differential equations
65L12 Finite difference and finite volume methods for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems
92D25 Population dynamics (general)
65L20 Stability and convergence of numerical methods for ordinary differential equations
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