A nonstandard finite-difference scheme for the Lotka–Volterra system Original Research Article

Most numerical integration schemes for the Lotka–Volterra system have the property that the computed solutions spiral when in fact the actual solutions are periodic corresponding to closed curves. We show that a direct application of the nonstandard methods of Mickens allows the construction of a finite-difference scheme that is dynamically consistent with the differential equations. Numerical results are given to support this result.