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**Exact finite-difference schemes for first order differential equations having three distinct fixed-points.**
*(English)*
Zbl 1131.65061

Summary: We construct nonstandard finite-difference (NSFD) schemes that provide exact numerical methods for a first-order differential equation having three distinct fixed-points. An explicit, but also nonexact, NSFD scheme is also constructed. It has the feature of preserving the critical properties of the original differential equation such as the positivity of the solutions and the stability behavior of the three fixed-points.

### MSC:

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 |

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\textit{L.-I. W. Roeger} and \textit{R. E. Mickens}, J. Difference Equ. Appl. 13, No. 12, 1179--1185 (2007; Zbl 1131.65061)

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