Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

Al-Mazmumy, M.; Alsulami, Aishah A.

doi:10.4236/jamp.2023.111007

Cited by 3 publications

(3 citation statements)

References 23 publications

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“…The traditional ADM is an energetic semi-analytical and, at the same time, numerical method for solving different forms of both linear and nonlinear ordinary and partial differential equations [10][11][12][13][14][15][16][17][18][19]. Thus, we shall be applying this traditional method to a generalized third-order nonlinear IVP in what follows.…”

Section: Traditional Adm For Third-order Nonlinear Ivpsmentioning

confidence: 99%

“…Subsequently, Attili and Syam [8] proposed a combination of the Adomian decomposition method (ADM) and the shooting method to numerically examine second-order linear and nonlinear BVPs using a special integration operator; the same method was equally extended to third-order linear BVPs by Alzahrani et al [9]. Additionally, we also cite [10][11][12][13][14][15][16][17][18][19] and the references therein for some relevant considerations through the ADM, and also refer the reader(s) to [20][21][22][23] for certain deliberations on the shooting approach.…”

Section: Introductionmentioning

confidence: 99%

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Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method

Alzahrani,

Alzaid,

Bakodah

et al. 2024

Axioms

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The present manuscript proposes a computational approach to efficiently tackle a class of two-point boundary value problems that features third-order nonlinear ordinary differential equations. Specifically, this approach is based upon a combination of the shooting method with a modification of the renowned Adomian decomposition method. The approach starts by transforming the governing BVP into two appropriate initial-value problems, and thereafter, solves the resulting IVPs recurrently. In addition, the application of this method to varied test models remains feasible—of course, this is supported by the competing Runge–Kutta method, among others, and reported through comparison plots and tables.

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Section: Traditional Adm For Third-order Nonlinear Ivpsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method

Alzahrani,

Alzaid,

Bakodah

et al. 2024

Axioms

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“…Additionally, differential transform method for Gauss Hypergeometric equation and Laguerre equations is applied in [23]. As well, the Frobenius method around all regular singular points for κ-Hypergeometric equation is employed in [24], Recently, [25] [26] thoroughly discussed the technique for obtaining an exact solution based on the modified Adomian decomposition method for the Laguerre equations and Chebyshev's differential equation.…”

Section: Introductionmentioning

confidence: 99%

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

Alsulami,

Al-Mazmumy,

Bakodah

et al. 2023

AJCM

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The current manuscript makes use of the prominent iterative procedure, called the Adomian Decomposition Method (ADM), to tackle some important special differential equations. The equations of curiosity in this study are the singular equations that arise in many physical science applications. Thus, through the application of the ADM, a generalized recursive scheme was successfully derived and further utilized to obtain closed-form solutions for the models under consideration. The method is, indeed, fascinating as respective exact analytical solutions are accurately acquired with only a small number of iterations.

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Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform

Alrebdi

Al-Jeaid

2023

Mathematics

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The Pantograph equation is a fundamental mathematical model in the field of delay differential equations. A special case of the Pantograph equation is well known as the Ambartsumian delay equation which has a particular application in Astrophysics. In this paper, the Laplace transform is successfully applied to solve the Pantograph delay equation. The solution is obtained in a closed series form in terms of exponential functions. This closed form reduces to the corresponding solution in the relevant literature for the Ambartsumian delay equation as a special case. In addition, the convergence of the obtained series is proved theoretically and validated graphically. Furthermore, the accuracy of the numerical results are estimated through several computations of the residual errors. It is shown that such residuals tend to zero, even in a huge domain. The obtained results reveal that the Laplace transform is a powerful approach to solve linear delay differential equations, including the Pantograph model.

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Solution of Laguerre’s Differential Equations via Modified Adomian Decomposition Method

Cited by 3 publications

References 23 publications

Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method

Computational Approach to Third-Order Nonlinear Boundary Value Problems via Efficient Decomposition Shooting Method

On the Application of Adomian Decomposition Method to Special Equations in Physical Sciences

Accurate Solution for the Pantograph Delay Differential Equation via Laplace Transform

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