On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations

Al-Rawi, Ekhlass S.; Samarchi, Merna A.

doi:10.1155/2022/5638901

Cited by 4 publications

(6 citation statements)

References 17 publications

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“…In this section, the fnite diference method involves solving the DSW system by substituting the derivatives in ( 1) and ( 2) with central fnite diference derivatives as given in (7) and (9). Tis transformation converts the system into a set of regular algebraic equations that can be solved using standard methods to determine the values of certain variables.…”

Section: Methodsmentioning

confidence: 99%

“…To calculate the approximate value of the solution u(x i , t j ), we use (3) and the central fnite diference (7), and substituting them into (1), we get…”

Section: Mathematical Formulation Of the Efd Methods For The Dsw Systemmentioning

confidence: 99%

“…Tese advancements have signifcantly enhanced our grasp of intricate nonlinear phenomena and our capacity to address real-world challenges. For instance, methods such as the Adomian decomposition method with modifed Bernstein polynomials [5], Bernstein polynomials in conjunction with artifcial neural networks [6], and the Elzaki decomposition method for tackling higher-order integrodiferential equations have all contributed to this progress [7][8][9][10][11][12][13][14]. Te formula for the Drinfeld's-Sokolov-Wilson (DSW) system also plays a critical role in this context [14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Younis,

Al-Rawi

2023

International Journal of Mathematics and Mathematical Sciences

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This study presents a new algorithm for effectively solving the nonlinear coupled Drinfeld’s–Sokolov–Wilson (DSW) system using a hybrid explicit finite difference technique with the Adomian polynomial (EFD-AP). The suggested approach addresses the problem of accurately solving the DSW system. Numerical results are obtained by comparing the exact solution with absolute and mean square errors using a test problem to assess the EFD-AP accuracy against the exact solution and the conventional explicit finite difference (EFD) method. The results exhibit excellent agreement between the approximate and exact solutions at different time values, and the results showed that the proposed EFD-AP method achieves superior accuracy and efficiency compared to the EFD method, which makes it a promising method for solving nonlinear partial differential systems of higher order.

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Section: Methodsmentioning

confidence: 99%

“…To calculate the approximate value of the solution u(x i , t j ), we use (3) and the central fnite diference (7), and substituting them into (1), we get…”

Section: Mathematical Formulation Of the Efd Methods For The Dsw Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Younis,

Al-Rawi

2023

International Journal of Mathematics and Mathematical Sciences

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“…Elzaki transform was first introduced by Tarig Elzaki [ 20 ]. Adomian decomposition method [ 21 ] is a well-known mathematical technique to solve the nonlinear partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Sadaf,

Perveen,

Akram

et al. 2024

PLoS ONE

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In this article, Elzaki decomposition method (EDM) has been applied to approximate the analytical solution of the time-fractional gas-dynamics equation. The time-fractional derivative is used in the Caputo-Fabrizio sense. The proposed method is implemented on homogenous and non-homogenous cases of the time-fractional gas-dynamics equation. A comparison between the exact and approximate solutions is also provided to show the validity and accuracy of the technique. A graphical representation of all the retrieved solutions is shown for different values of the fractional parameter. The time development of all solutions is also represented in 2D graphs. The obtained results may help understand the physical systems governed by the gas-dynamics equation.

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“…Several intellectuals have created a variety of analytical integral transform techniques for precise and approximated answers during the past few years, including the Laplace transform method [25,26], Shehu transform method [27,28], Aboodh transform method [22], Sumudu transform method [29], Elzaki transform method [30], and Mohand transform method [17]. The Sumudu transform method is an integral like the Laplace transform method, introduced in the early 1990s by Watugala [31] to solve DEs and control engineering problems.…”

Section: Introductionmentioning

confidence: 99%

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

Moltot

Deresse

2022

Advances in Mathematical Physics

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In this study, an efficient analytical method called the Sumudu Iterative Method (SIM) is introduced to obtain the solutions for the nonlinear delay differential equation (NDDE). This technique is a mixture of the Sumudu transform method and the new iterative method. The Sumudu transform method is used in this approach to solve the equation’s linear portion, and the new iterative method’s successive iterative producers are used to solve the equation’s nonlinear portion. Some basic properties and theorems which help us to solve the governing problem using the suggested approach are revised. The benefit of this approach is that it solves the equations directly and reliably, without the prerequisite for perturbations or linearization or extensive computer labor. Five sample instances from the DDEs are given to confirm the method’s reliability and effectiveness, and the outcomes are compared with the exact solution with the assistance of tables and graphs after taking the sum of the first eight iterations of the approximate solution. Furthermore, the findings indicate that the recommended strategy is encouraging for solving other types of nonlinear delay differential equations.

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On the Use of Elzaki Decomposition Method for Solving Higher-Order Integro-Differential Equations

Cited by 4 publications

References 17 publications

Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Improved Finite Difference Technique via Adomian Polynomial to Solve the Coupled Drinfeld’s–Sokolov–Wilson System

Solution of time-fractional gas dynamics equation using Elzaki decomposition method with Caputo-Fabrizio fractional derivative

Approximate Analytical Solution to Nonlinear Delay Differential Equations by Using Sumudu Iterative Method

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