A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets

Mohammad, Mutaz; Trounev, Alexander

doi:10.1155/2022/1753992

Cited by 5 publications

(3 citation statements)

References 23 publications

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“…DDEs and NDDEs have been studied by many authors and various analytical and numerical methods have been proposed. Some of the numerical methods are New One-Step Technique (6) , Hybrid multistep block method (7) , Legendre pseudo spectral method (8) , Euler Wavelet method (9) , matrix method based on Clique polynomial (10) , Collocation Method based on successive integration technique (11).…”

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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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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“…This wavelet basis originated from a single function called the mother wavelet ψ(x), which is a small beat. In literature, wavelet methods such as the Euler wavelet scheme for volterra delay integral DEs [14], Hermite wavelet scheme for nonlinear singular initial value problems (IVPs) [15], Legendre wavelet method for nonlinear DDEs [16], continuous wavelet series method for Lane-Emden equations [17], B-spline method for Burgers-Huxley equation [18], Haar wavelet method for the Chen-Lee-Liu equation [19], DDEs based on Euler wavelets [20], R-K method for the DDEs [21] and A novel approach for Pantograph equations [22], and so on [23,24] have been presented.…”

Section: Introductionmentioning

confidence: 99%

Wavelets approach for the solution of nonlinear variable delay differential equations

Kumbinarasaiah

Mundewadi

2023

International Journal of Mathematics and Computer in Engineering

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In this study, the Laguerre wavelet-oriented numerical scheme for nonlinear first and second-order delay differential equations (DDEs) is offered. The proposed technique is dependent on the truncated series of the Laguerre wavelets approximation of an unknown function. Here, we transform the different ordered DDEs into a system of non-linear algebraic equations with the help of limit points of a sequence of collocation points. Four nonlinear illustrations are involved to prove the efficiency of the planned technique. Obtained results are equated with the current results, indicating the proposed technique’s accuracy and efficiency.

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“…Maleki and Davari (2021) present adaptive collocation methods and examine the convergence properties of the method. Recently, Mohammad and Trounev (2022) proposed the use of Euler wavelets for numerical solution of NNDEs. The authors of Ferranti et al (2017) use stochastic collocation to assess parameter variability in PEEC circuits.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of neutral delay differential equations with high-frequency inputs

Condon

2023

COMPEL

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Purpose The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved. Design/methodology/approach The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases. Findings An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation. Originality/value The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

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A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets

Cited by 5 publications

References 23 publications

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

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

Wavelets approach for the solution of nonlinear variable delay differential equations

Numerical analysis of neutral delay differential equations with high-frequency inputs

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