Oscillation Analysis Algorithm for Nonlinear Second-Order Neutral Differential Equations

Liang Song (), Shaodong Chen and Guoxin Wang
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Liang Song: School of Mathematics and Physics, Nanyang Institute of Technology, Nanyang 473004, China
Shaodong Chen: School of Mathematics and Physics, Nanyang Institute of Technology, Nanyang 473004, China
Guoxin Wang: School of Mathematics and Physics, Nanyang Institute of Technology, Nanyang 473004, China

Mathematics, 2023, vol. 11, issue 16, 1-14

Abstract: Differential equations are useful mathematical tools for solving complex problems. Differential equations include ordinary and partial differential equations. Nonlinear equations can express the nonlinear relationship between dependent and independent variables. The nonlinear second-order neutral differential equations studied in this paper are a class of quadratic differentiable equations that include delay terms. According to the t-value interval in the differential equation function, a basis is needed for selecting the initial values of the differential equations. The initial value of the differential equation is calculated with the initial value calculation formula, and the existence of the solution of the nonlinear second-order neutral differential equation is determined using the condensation mapping fixed-point theorem. Thus, the oscillation analysis of nonlinear differential equations is realized. The experimental results indicate that the nonlinear neutral differential equation can analyze the oscillation behavior of the circuit in the Colpitts oscillator by constructing a solution equation for the oscillation frequency and optimizing the circuit design. It provides a more accurate control for practical applications.

Keywords: nonlinear; second order; neutral differential equation; vibration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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