Applied Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld–Sokolov–Wilson System

Al-Rozbayani, Abdulghafor M.; Ali, Ammar Yaser

doi:10.33899/csmj.2021.170017

Cited by 3 publications

(3 citation statements)

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“…Combining these techniques can be used to simplify the complexity of equations and make the solution process easier. Additionally, it can be applied for the precise determination of various systems [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

Mustafa

2023

Computational and Mathematical Methods

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The Sumudu transform is presented in this paper in a modified form which is aimed at improving its performance and employing it along with a modified iteration method in order to determine the solution to a system of nonlinear partial differential equations. This includes a theoretical analysis of the associated modified Sumudu transform. It also includes an explanation of the mathematical method for utilizing the transform in conjunction with the modified iteration technique. The iteration method is employed to determine the nonlinear terms of the equations. The research is valuable in the sense that it allows approximate and exact solution configurations to be determined by combining the modified Sumudu transform with a modified iteration method. As another benefit, the modified Sumudu transform can be developed and enhanced to be applicable to a wide range of equations, making it an effective solution tool. By combining techniques, a final advantage is that the solutions can be derived quickly and easily as a result of the combined approach. Finally, an old transformation which has been modified from the Sumudu transform is combined with the modified iteration method to examine its capability of yielding convergent solutions by incorporating the modified iteration method into it.

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Section: Introductionmentioning

confidence: 99%

Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

Mustafa

2023

Computational and Mathematical Methods

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“…This approach provides a powerful tool for finding approximate solutions for the system [13]. Rozbayani and Ali explored the system under a combination of Sumudu transform and Adomian decomposition method [14]. Recently, the fractional DSW system has been examined with Mittage-Laffler type kernels and exponential decay.…”

Section: Introductionmentioning

confidence: 99%

A Comparative Study of Time Fractional Nonlinear Drinfeld–Sokolov–Wilson System via Modified Auxiliary Equation Method

Akram,

Sadaf,

Zainab

et al. 2023

Fractal Fract

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The time-fractional nonlinear Drinfeld–Sokolov–Wilson system, which has significance in the study of traveling waves, shallow water waves, water dispersion, and fluid mechanics, is examined in the presented work. Analytic exact solutions of the system are produced using the modified auxiliary equation method. The fractional implications on the model are examined under β-fractional derivative and a new fractional local derivative. Extracted solutions include rational, trigonometric, and hyperbolic functions with dark, periodic, and kink solitons. Additionally, by specifying values for fractional parameters, graphs are utilized to comprehend the fractional effects on the obtained solutions.

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“…Researchers combined two powerful methods to develop a new method for solving FODEs. Some of these groups are described as a combination of the Adomian decomposition method and the Sumudu transform [54], as well as the homotopy analysis method and the natural transform [55] and the Laplace transformation with homotopy perturbation approach [56]. In this study, we applied the novel combined technique, known as the ERPSM, to provide approximate and exact solutions for FMPS and PDEs.…”

Section: Introductionmentioning

confidence: 99%

A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay

Liaqat

Khan

Akgül

et al. 2022

Journal of Function Spaces

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Some researchers have combined two powerful techniques to establish a new method for solving fractional-order differential equations. In this study, we used a new combined technique, known as the Elzaki residual power series method (ERPSM), to offer approximate and exact solutions for fractional multipantograph systems (FMPS) and pantograph differential equations (PDEs). In Caputo logic, the fractional-order derivative operator is measured. The Elzaki transform method and the residual power series method (RPSM) are combined in this novel technique. The suggested technique is based on a new version of Taylor’s series that generates a convergent series as a solution. Establishing the coefficients for a series, like the RPSM, necessitates computing the fractional derivatives each time. As ERPSM just requires the concept of a zero limit, we simply need a few computations to get the coefficients. The novel technique solves nonlinear problems without the need for He’s and Adomian polynomials, which is an advantage over the other combined methods based on homotopy perturbation and Adomian decomposition methods. The relative, recurrence, and absolute errors of the problems are analyzed to evaluate the efficiency and consistency of the presented method. Graphical significances are also identified for various values of fractional-order derivatives. As a result, the procedure is quick, precise, and easy to implement, and it yields outstanding results.

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Applied Sumudu Transform with Adomian Decomposition Method to the Coupled Drinfeld–Sokolov–Wilson System

Cited by 3 publications

References 0 publications

Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

Employing a Modified Sumudu with a Modified Iteration Method to Solve the System of Nonlinear Partial Differential Equations

A Comparative Study of Time Fractional Nonlinear Drinfeld–Sokolov–Wilson System via Modified Auxiliary Equation Method

A Novel Numerical Technique for Fractional Ordinary Differential Equations with Proportional Delay

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