# On the Construction of Exact Numerical Schemes for Linear Delay Models

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## Abstract

**:**

## 1. Introduction

## 2. Methods and Results

**Lemma**

**1.**

**Theorem**

**1.**

**Proof.**

**Theorem**

**2.**

**Proof.**

**Theorem**

**3.**

**Proof.**

**Corollary**

**1.**

**Remark**

**1.**

**Example**

**1.**

## 3. Discussion

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

ODE | Ordinary Differential Equation(s) |

OΔE | Ordinary Difference Equation(s) |

NSFD | Nonstandard Finite Difference |

DDE | Delay Differential Equation(s) |

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**Figure 1.**Exact continuous solution (lines) and exact numerical solution computed with the scheme given in Corollary 1 (circles) for problem (1) with the parameters $\gamma =3/4$, $\alpha =-4$, $\beta =1/2$, $\tau =1$, and with the initial function $\phi \left(t\right)={(t+1)}^{2}$ (red).

**Figure 2.**Exact continuous solution (lines) and exact numerical solution computed with the scheme given in Corollary 1 (circles) for problem (1) with the parameters $\gamma =1$, $\alpha =-1$, $\beta =1.1$, $\tau =1$, and with the initial function $\phi \left(t\right)={(t+1)}^{2}$ (red).

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**MDPI and ACS Style**

Mayorga, C.J.; Castro, M.Á.; Sirvent, A.; Rodríguez, F.
On the Construction of Exact Numerical Schemes for Linear Delay Models. *Mathematics* **2023**, *11*, 1836.
https://doi.org/10.3390/math11081836

**AMA Style**

Mayorga CJ, Castro MÁ, Sirvent A, Rodríguez F.
On the Construction of Exact Numerical Schemes for Linear Delay Models. *Mathematics*. 2023; 11(8):1836.
https://doi.org/10.3390/math11081836

**Chicago/Turabian Style**

Mayorga, Carlos Julio, María Ángeles Castro, Antonio Sirvent, and Francisco Rodríguez.
2023. "On the Construction of Exact Numerical Schemes for Linear Delay Models" *Mathematics* 11, no. 8: 1836.
https://doi.org/10.3390/math11081836