Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay

Loucif, Sami; Guefaifia, Rafik; Zitouni, Salah; Khochemane, Houssem Eddine

doi:10.1007/s00033-023-01972-4

Cited by 5 publications

(4 citation statements)

References 40 publications

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“…𝑇 0 (𝑡) and 𝑇 1 (𝑡) can be obtained from Eqn. (5). Then the remaining terms are determined by from Eqn.…”

Section: Chebyshev Polynomialmentioning

confidence: 99%

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Solving neutral delay differential equations using least square method based on successive integration technique

C. Kayelvizhi,

A. Emimal Kanaga Pushpam

2024

Int. J. Sci. Res. Arch.

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The main objective of this work is to propose the Least square method (LSM) using successive integration technique for solving Neutral delay differential equations (NDDEs). Continuous LSM and Discrete LSM have been presented by adopting different orthogonal polynomials as weighted basis functions. In this study, the most widely used classical orthogonal polynomials, namely, the Bernoulli polynomial, the Chebyshev polynomial, the Hermite polynomial, and the Fibonacci polynomial are considered. Numerical examples of linear and nonlinear NDDEs have been provided to demonstrate the efficiency and accuracy of the method. Approximate solutions obtained by the proposed method are well comparable with exact solutions. From the results it is observed that the accuracy of the numerical solutions by the proposed method increases as N (order of the polynomial) increases. The proposed method is very effective, simple, and suitable for solving the linear and nonlinear NDDEs in real-world problems.

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“…𝑇 0 (𝑡) and 𝑇 1 (𝑡) can be obtained from Eqn. (5). Then the remaining terms are determined by from Eqn.…”

Section: Chebyshev Polynomialmentioning

confidence: 99%

“…DDEs and NDDEs arise in the fields of signal processing, digital images, control systems, epidemiology, chemical kinetics, etc. Some notable applications of DDEs and NDDEs are in electrochemical biosensor [1], cancer cells growth [2] and population model [3], human balancing models [4], quasistatic piezoelectric beams [5].…”

Section: Introductionmentioning

confidence: 99%

Solving neutral delay differential equations using least square method based on successive integration technique

C. Kayelvizhi,

A. Emimal Kanaga Pushpam

2024

Int. J. Sci. Res. Arch.

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show abstract

“…T 0 (t) and T 1 (t) can be obtained from Equation (5). Then the remaining terms are determined from Equation (6).…”

Section: Chebyshev Polynomialmentioning

confidence: 99%

“…DDEs arise in the field of signal processing, digital images, control system, epidemiology, chemical kinetics, etc. https://www.indjst.org/ Some notable applications of DDEs and NDDEs are in electrochemical biosensor (1) , cancer cells growth (2) and population model (3) , human balancing models (4) , quasi-static piezoelectric beams (5) .…”

Section: Introductionmentioning

confidence: 99%

Solving Neutral Delay Differential Equations Using Galerkin Weighted Residual Method Based on Successive Integration Technique and its Residual Error Correction

Kayelvizhi,

Pushpam

2024

IJST

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Objectives: The main objectives of this work are to solve Neutral Delay Differential Equations (NDDEs) using Galerkin weighted residual method based on successive integration technique and to obtain the Estimation of Error using Residual function. Methods: The Galerkin weighted residual method based on successive integration technique is proposed to obtain approximate solutions of the NDDEs. In this study, the most widely used classical orthogonal polynomials, namely, the Bernoulli polynomials, the Chebyshev polynomials, the Hermite polynomials, and the Fibonacci polynomials are considered. Findings: Numerical examples of linear and nonlinear NDDEs have been considered to demonstrate the efficiency and accuracy of the method. Approximate solutions obtained by the proposed method are well comparable with exact solutions. Novelty: From the results it is observed that the accuracy of the numerical solutions by the proposed method increases as N increases. The proposed method is very effective, simple, and suitable for solving the linear and nonlinear NDDEs in real-world problems. Keywords: Galerkin Weighted Residual method, Polynomials, Hermite, Bernoulli, Chebyshev, Fibonacci, Successive integration technique, Neutral Delay Differential Equations

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Well-posedness and general energy decay for a nonlinear piezoelectric beams system with magnetic and thermal effects in the presence of distributed delay

Messaoudi,

Douib,

Zitouni

2024

Journal of Thermal Stresses

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Global well-posedness and exponential decay of fully dynamic and electrostatic or quasi-static piezoelectric beams subject to a neutral delay

Cited by 5 publications

References 40 publications

Solving neutral delay differential equations using least square method based on successive integration technique

Solving neutral delay differential equations using least square method based on successive integration technique

Solving Neutral Delay Differential Equations Using Galerkin Weighted Residual Method Based on Successive Integration Technique and its Residual Error Correction

Well-posedness and general energy decay for a nonlinear piezoelectric beams system with magnetic and thermal effects in the presence of distributed delay

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