A reliable modification of Adomian decomposition method

Wazwaz, Abdul‐Majid

doi:10.1016/s0096-3003(98)10024-3

Cited by 524 publications

(287 citation statements)

References 9 publications

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“…Here we just consider the basic points of this method, further details can be found in [23]. We first consider the equation…”

Section: Adomian Decomposition Methods (Adm)mentioning

confidence: 99%

Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations

Deni̇z¹,

Bıldık²

2014

IJMO

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Abstract-In this paper, we will present a comparison between the Adomian Decomposition Method (ADM) and Taylor Matrix Method by solving some well-known partial differential equations (PDEs). In order to illustrate the analysis we examined the Telegraph equation, which is considered one of the most significant partial differential equations, describe wave propagation of electric signals in a cable transmission line and Klein-Gordon equation which is encountered in several applied physics fields such as, quantum field theory , fluid dynamics , optoelectronic devices design and numerical analysis. Our study shows that the decomposition method is faster and easy to use from a computational viewpoint.Index Terms-Adomian decomposition method, Klein gordon equation, taylor matrix method, telegraph equation.

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“…Here we just consider the basic points of this method, further details can be found in [23]. We first consider the equation…”

Section: Adomian Decomposition Methods (Adm)mentioning

confidence: 99%

Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations

Deni̇z¹,

Bıldık²

2014

IJMO

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“…and the iterates defined using the Modified Technique [20] are determined in the following recursive way: …”

Section: Analysis Of the Methodsmentioning

confidence: 99%

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

Al-Hayani¹

2014

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In this paper, the Adomian decomposition method with Green's function (Standard Adomian and Modified Technique) is applied to solve linear and nonlinear tenth-order boundary value problems with boundary conditions defined at any order derivatives. The numerical results obtained with a small amount of computation are compared with the exact solutions to show the efficiency of the method. The results show that the decomposition method is of high accuracy, more convenient and efficient for solving high-order boundary value problems.

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“…Adomian's decomposition method (ADM) is useful and powerful method for solving linear and nonlinear functional equations [11][12][13]. Recently a great deal of interest has been focused on the application of Adomian's decomposition method to solve a wide variety of stochastic and terministic problems [14,15].…”

Section: T a T G T X T K T S F S X S S T A Bmentioning

confidence: 99%

The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations

Bakodah¹

2012

AJCM

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A reliable modification of Adomian decomposition method

Cited by 524 publications

References 9 publications

Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations

Comparison of Adomian Decomposition Method and Taylor Matrix Method in Solving Different Kinds of Partial Differential Equations

Adomian Decomposition Method with Green’s Function for Solving Tenth-Order Boundary Value Problems

The Appearance of Noise Terms in Modified Adomian Decomposition Method for Quadratic Integral Equations

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