A continuous solution of solving a class of nonlineartwo point boundary value problem using Adomian decomposition method

El‐Kalla, I. L.; Mhlawy, Ashraf M. El; Botros, Monica

doi:10.1016/j.asej.2018.11.002

Cited by 14 publications

(4 citation statements)

References 17 publications

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“…The Adomian decomposition method was introduced in 1970s by George Adomian [30]. This method is used widely ever since to solve nonlinear (ordinary or partial) differential equations, integral equations, as well as integro-differential equations, see [31][32][33][34][35] and the references therein. The solution obtained by this method has a series form which is rapidly convergent and easy to compute, assuming that we deal with analytic functions, see [36][37][38].…”

Section: The Methodologymentioning

confidence: 99%

Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

2019

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This work deals with a new modified version of the Adomian-Rach decomposition method (MDM). The MDM is based on combining a series solution and decomposition method for solving nonlinear differential equations with Adomian polynomials for nonlinearities. With application to a class of nonlinear oscillators known as the Lienard-type equations, convergence and error analysis are discussed. Several physical problems modeled by Lienard-type equations are considered to illustrate the effectiveness, performance and reliability of the method. In comparison to the 4th Runge-Kutta method (RK4), highly accurate solutions on a large domain are obtained.

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Section: The Methodologymentioning

confidence: 99%

Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

2019

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“…Also, many modifications were made to this method by numerous researchers in an attempt to improve the accuracy or extend the applications of this method [1,2,6,11,19]. Also, El-Kalla polynomial was discussed by El-Kalla In [13,14,15,16,17,18], and conclude that El-kalla polynomial was directly used to estimate the maximum absolute truncated error of the Adomian series solution which cannot be estimated using the traditional polynomials.…”

Section: Convergence Remarksmentioning

confidence: 99%

Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method

Elmahdy

Sayed

Abdelgaber

et al. 2020

Engineering Research Journal

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In this work, we proposed a reliable polynomials called El-kalla polynomials which are faster than the traditional Adomian polynomials in solving some classes of nonlinear differential equations by Adomian decomposition method (ADM). The main advantages of El-kalla polynomials can be summerized in the following main three points:  El-kalla polynomials are recursive and do not have derivative terms so, El-kalla formula is easy in programming and save much time on the same processor compared with the traditional Adomian polynomials formula. Solution using El-Kalla polynomials converges faster than the traditional Adomian polynomials. El-Kalla polynomials used directly in estimating the maximum absolute truncated error of the series solution. Some convergence remarks are studied and some numerical examples are solved to verify the above advantages. In all applied cases, we obtained an excellent performance that may lead to a promising approach for many applications.

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“…The Adomian decomposition manner was introduced by Grorge Adomian in (1970) [3]. This method is used widely for solving non-linear ordinary differential equation [5]. The solution get by this manner has a series shape which convergent and easy accounting process.…”

Section: Introductionmentioning

confidence: 99%

New Development of Adomian Decomposition Method for Solving Second Order Ordinary Differential Equations

Al-Mekhlfi

Hasan

2023

EIJMS

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This study attempts at Adomian Decomposition Method (ADM) for solving second order ordinary differential equations such as Multi singular equation, Bessel’s equation, and Oscillatory systems. The (ADM) results in many known equations, some of them are studied and investigated by mathematicians and researchers, while others are still not well researched yet. We give a new differential operator and invers differential operator to solve different types for initial value problem in the second order ordinary differential equation. There are some different situations that we will study and give the non-linear examples that lead us to the approximate solutions of exact solution.

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A continuous solution of solving a class of nonlineartwo point boundary value problem using Adomian decomposition method

Cited by 14 publications

References 17 publications

Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

Numeric-Analytic Solutions for Nonlinear Oscillators via the Modified Multi-Stage Decomposition Method

Solution of a class of nonlinear differential equations using an accelerated version of Adomian decomposition method

New Development of Adomian Decomposition Method for Solving Second Order Ordinary Differential Equations

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