<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>The oscillation theory of differential equations is an important branch of performance of differential equations, which is widely used in engineering control, vibration mechanics, mechanics, and industry. Therefore, the vibration performance of different parts has attracted people’s attention, and a lot of research work has been done. For a special class of delay differential equations - advanced piecewise continuous differential equations, the oscillation of numerical solution is discussed. The <italic>θ</italic> − method is used to discretize the equation, and the numerical method is obtained to keep the oscillation of the analytical solution of the equation, progressive conditions. At the same time, four different states of the dynamic behavior are discussed in detail for the analytical solution and the numerical solution respectively. Some numerical examples further verify the corresponding conclusions.</p>
</abstract>

The oscillation theory of differential equations is an important branch of performance of differential equations, which is widely used in engineering control, vibration mechanics, mechanics, and industry. Therefore, the vibration performance of different parts has attracted people’s attention, and a lot of research work has been done. For a special class of delay differential equations - advanced piecewise continuous differential equations, the oscillation of numerical solution is discussed. The θ − method is used to discretize the equation, and the numerical method is obtained to keep the oscillation of the analytical solution of the equation, progressive conditions. At the same time, four different states of the dynamic behavior are discussed in detail for the analytical solution and the numerical solution respectively. Some numerical examples further verify the corresponding conclusions.

Oscillation and Asymptotic Behavior of a Special Delay Third Order Nonlinear Neutral Functional Differential Equation

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

The oscillation theory of differential equations is an important branch of performance of differential equations, which is widely used in engineering control,...

Oscillation and Asymptotic Behavior of a Special Delay Third Order Nonlinear Neutral Functional Differential Equation

Published Online: Jun 19, 2023

Page range: 2463 - 2474

Received: Jul 19, 2022

Accepted: Dec 23, 2022

DOI: https://doi.org/10.2478/amns.2023.1.00427

Keywords
Third order differential equation, Asymptotic property, Vibration, Nonvibration

© 2023 Zhimin Luo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Oscillation and Asymptotic Behavior of a Special Delay Third Order Nonlinear Neutral Functional Differential Equation

Published Online: Jun 19, 2023

Page range: 2463 - 2474

Received: Jul 19, 2022

Accepted: Dec 23, 2022

DOI: https://doi.org/10.2478/amns.2023.1.00427

KeywordsThird order differential equation, Asymptotic property, Vibration, Nonvibration

© 2023 Zhimin Luo et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Third order differential equation, Asymptotic property, Vibration, Nonvibration