Application of Modified Adomian Decomposition Method to (2+1)-dimensional Non-linear Wu-Zhang system

Qasim, Ahmed Farooq; Ali, Zead Y.

doi:10.29304/jqcm.2018.10.1.340

Cited by 7 publications

(3 citation statements)

References 6 publications

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“…To obtain the exact solution, this is one of the most critical topics in mathematical physics. Several authors have recently used various numerical and analytical approaches to find the numerical and analytical solution to the WZ equations, for example, using the first integral method [21], the modified Adomian decomposition method [22], the homotopy perturbation method [23], the extended Tanh method and the exp-function method [24], the exponential rational function method [25], the successive approximation method [26], the modified variation iteration method [27], the extended trial equation method [28] and the dynamic system method [29]. In addition, more solitonic solutions were extracted using the mapping method.…”

Section: Introductionmentioning

confidence: 99%

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Yasmin,

Alderremy,

Shah

et al. 2024

Front. Phys.

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In this study, we employ the effective iterative method to address the fractional Wu-Zhang Equation within the framework of the Caputo Derivative. The effective iterative method offers a practical approach to obtaining approximate solutions for fractional differential equations. We seek to provide insights into its solution and behavior by applying this method to the Wu-Zhang Equation. Through numerical analysis and the presentation of relevant tables and Figures, we demonstrate the accuracy and efficiency of this method in solving the fractional Wu-Zhang Equation. This research contributes to the understanding and solution of fractional-order differential equations and their applications in various scientific and engineering domains.

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Section: Introductionmentioning

confidence: 99%

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Yasmin,

Alderremy,

Shah

et al. 2024

Front. Phys.

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“…[17]. However, some researchers have used the MADM method to solve the following issues: partial differential equations (Burgers equation) [18], generalized fifth-order Korteweg-de Vries (GFKdV) equation [19], for finding exact solutions of nonlinear integral equations [17], dimensional (2+1) for nonlinear system Wu-Zhang [20].…”

Section: Introductionmentioning

confidence: 99%

“…Al-Amr compares Adomian's decomposition method and Variational iteration method of a Reaction-Diffusion System with fast reversible reaction [23]. Qasim applied (ADM) for nonlinear Wu Zhang system and compared the solution with MVIM, HPM, and RDTM [20]. Firoozjae compares the adomian decomposition method and differential quadrature method for solving some nonlinear partial differential equations [24].…”

Section: Introductionmentioning

confidence: 99%

Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

Salim

Jasim²,

Ali³

2021

IJEECS

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<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution. Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

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An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

Patel¹,

Patel

2022

Math Methods in App Sciences

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This paper considers time‐fractional false(2+1false)$$ \left(2+1\right) $$‐dimensional Wu–Zhang nonlinear system of partial differential equation describing a long dispersive wave. An approximate analytical solution of the dispersion relation of the long wave has been obtained by the fractional reduced differential transform method (FRDTM). The effect of fractional‐order α$$ \alpha $$ on the wave profile of the solution is discussed graphically and comparing the exact solution of Wu–Zhang equation when α=1$$ \alpha =1 $$. The result shows that the present method reveals the effectiveness, efficiency, and reliability of computed mathematical results to easily solve the fractional‐order Wu–Zhang (WZ) system of differential equations.

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Application of Modified Adomian Decomposition Method to (2+1)-dimensional Non-linear Wu-Zhang system

Cited by 7 publications

References 6 publications

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Iterative solution of the fractional Wu-Zhang equation under Caputo derivative operator

Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

An analytical approach to solve the fractional‐order (2 + 1)‐dimensional Wu–Zhang equation

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