### Abstract

One-dimensional models are important for developing, demonstrating and testing new methods and approaches, which can be extended to more complex systems. We design for a linear delay differential equation a reliable numerical method, which consists of two time splits as follows: (a) It is an exact scheme at the early time evolution -τ≤t≤τ, where τ is the discrete value of the delay; (b) Thereafter, it is a nonstandard finite difference (NSFD) scheme obtained by suitable discretizations at the backtrack points. It is shown theoretically and computationally that the NSFD scheme is dynamically consistent with respect to the asymptotic stability of the trivial equilibrium solution of the continuous model. Extension of the NSFD to nonlinear epidemiological models and its good performance are tested on a numerical example.

Original language | English (US) |
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Article number | 20728 |

Pages (from-to) | 388-403 |

Number of pages | 16 |

Journal | Applied Mathematics and Computation |

Volume | 258 |

DOIs | |

State | Published - May 1 2015 |

### Keywords

- Delay differential equations
- Dynamic stability
- Exact scheme
- Nonstandard finite difference scheme

### ASJC Scopus subject areas

- Computational Mathematics
- Applied Mathematics

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## Cite this

*Applied Mathematics and Computation*,

*258*, 388-403. [20728]. https://doi.org/10.1016/j.amc.2015.01.088