A comparative study of Adomain decomposition method and the new integral transform “Elzaki transform’’

Adam, Badradeen

doi:10.14419/ijamr.v4i1.3799

Cited by 2 publications

(2 citation statements)

References 16 publications

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“…Through examples, it has been shown that the approximate solutions acquired by trapezoidal rule are in good agreement with exact solutions obtained through transformation method. [4] conducted comparative study between Adomian Decomposition Method (ADM) and Elzaki transform. Both methods have been used to solve linear partial differential equations with constant coefficients.…”

Section: Literature Reviewmentioning

confidence: 99%

Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations

Sharjeel¹,

Barakzai²

2019

JAMP

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Volterra type integral equations have diverse applications in scientific and other fields. Modelling physical phenomena by employing integral equations is not a new concept. Similarly, extensive research is underway to find accurate and efficient solution methods for integral equations. Some of noteworthy methods include Adomian Decomposition Method (ADM), Variational Iteration Method (VIM), Method of Successive Approximation (MSA), Galerkin method, Laplace transform method, etc. This research is focused on demonstrating Elzaki transform application for solution of linear Volterra integral equations which include convolution type equations as well as one system of equations. The selected problems are available in literature and have been solved using various analytical, semi-analytical and numerical techniques. Results obtained after application of Elzaki transform have been compared with solutions obtained through other prominent semi-analytic methods i.e. ADM and MSA (limited to first four iterations). The results substantiate that Elzaki transform method is not only a compatible alternate approach to other analytic methods like Laplace transform method but also simple in application once compared with methods ADM and MSA.

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Section: Literature Reviewmentioning

confidence: 99%

Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations

Sharjeel¹,

Barakzai²

2019

JAMP

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“…Lately, to solve the linear system, Tarig M. Elzaki and Salih M. Elzaki produced a new integral transformation, it was Elzaki transform [23], which then used by Tarig [24] to solve common differential equations with more details. For the same purpose, Adam [25] conducted a comparative investigation between two methods, i.e. Adomain Decomposition and Elzaki Transform, and reported that both techniques were powerful and efficient.…”

Section: Introductionmentioning

confidence: 99%

Solving the Vibrating Spring Equation Using Fuzzy Elzaki Transform

Khudair¹,

Alkiffai²,

Albukhuttar³

2020

MMEP

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In this article, a fuzzy Elzaki transform (FZT) is discussed in the context of highly-generalized differentiability concepts, where a new formula of fuzzy derivatives for the fuzzy Elzaki transform is derived as well. It shows the applicability of this interesting fuzzy transform for solving differential equations with constant coefficients also for its computational power. Since ordinary linear equations are mostly used in physical fields, the motion of a mass on a vibrating spring problem is solved by using this kind of fuzzy Elzaki transform.

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A comparative study of Adomain decomposition method and the new integral transform “Elzaki transform’’

Abstract: In this article, we present a comparative study between Adomain decomposition method and the new integral transform "Elzaki Transform". We use the methods to solve the linear Partial differential equations with constant coefficients.

Cited by 2 publications

References 16 publications

Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations

Some New Applications of Elzaki Transform for Solution of Linear Volterra Type Integral Equations

Solving the Vibrating Spring Equation Using Fuzzy Elzaki Transform

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