Numerical Solution of a Reaction-Diffusion System with Fast Reversible Reaction by Using Adomian’s Decomposition Method and He’s Variational Iteration Method

Al-Sawoor, Ann J.; Al‐Amr, Mohammed O.

doi:10.33899/csmj.2012.163715

Cited by 4 publications

(3 citation statements)

References 23 publications

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“…Recently, researchers applied different methods to obtain accurate, stable, and efficient analytical solutions of FOPDEs, such as operational matrix method, 12 Elzaki decomposition approach, 13 Aboodh decomposition method, 14 Sumudu decomposition method, 15 homotropy analysis method, 16 residual power series technique, 17 and pseudospectral method 18 . But most FOPDEs do not have analytic solutions; therefore, numerical simulations are used extensively like collocation scheme, 19 Adomian decomposition method, 20 Iterative method for Riemann‐Liouville fractional differential equation, 21–23 finite difference method, 24–26 variational iteration technique, 27 and finite element method 28 . Alesemi et al 29 introduced the novel iterative transform method and homotopy perturbation transform technique to compute the fractional order (Cauchy reaction‐diffusion equation [CRDE]).…”

Section: Introductionmentioning

confidence: 99%

“…technique, 17 and pseudospectral method. 18 But most FOPDEs do not have analytic solutions; therefore, numerical simulations are used extensively like collocation scheme, 19 Adomian decomposition method, 20 Iterative method for Riemann-Liouville fractional differential equation, [21][22][23] finite difference method, [24][25][26] variational iteration technique, 27 and finite element method. 28 Alesemi et al 29 introduced the novel iterative transform method and homotopy perturbation transform technique to compute the fractional order (Cauchy reaction-diffusion equation [CRDE]).…”

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confidence: 99%

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Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Ragb

Wazwaz

Mohamed

et al. 2023

Math Methods in App Sciences

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This paper aims to explore and apply differential quadrature based on different test functions to find an efficient numerical solution of fractional order Cauchy reaction-diffusion equations (CRDEs). The governing system is discretized through time and space via novel techniques of differential quadrature method and the fractional operator of Caputo kind. Two problems are offered to explain the accuracy of the numerical algorithms. To verify the reliability, accuracy, efficiency, and speed of these methods, computed results are compared numerically and graphically with the exact and semi-exact solutions. Then mainly, we deal with absolute errors and L ∞ errors to study the convergence of the presented methods. For each technique, MATLAB Code is designed to solve these problems with the error reaching ≤1 Â 10 À5 . In addition, a parametric analysis is presented to discuss influence of fractional order derivative on results. The achieved solutions prove the viability of the presented methods and demonstrate that these methods are easy to implement, effective, high accurate, and appropriate for studying fractional partial differential equations emerging in fields related to science and engineering.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Ragb

Wazwaz

Mohamed

et al. 2023

Math Methods in App Sciences

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“…Ranen compares the homotopy perturbation method to ADM; she solves some examples and illustrates the efficiency of the homotopy perturbation method [22]. 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].…”

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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New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method

Baskonus

Bulut

Sulaıman

2019

Applied Mathematics and Nonlinear Sciences

181

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In this paper, a powerful sine-Gordon expansion method (SGEM) with aid of a computational program is used in constructing a new hyperbolic function solutions to one of the popular nonlinear evolution equations that arises in the field of mathematical physics, namely; longren-wave equation. We also give the 3D and 2D graphics of all the obtained solutions which are explaining new properties of model considered in this paper. Finally, we submit a comprehensive conclusion at the end of this paper.

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Numerical Solution of a Reaction-Diffusion System with Fast Reversible Reaction by Using Adomian’s Decomposition Method and He’s Variational Iteration Method

Cited by 4 publications

References 23 publications

Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

Fractional differential quadrature techniques for fractional order Cauchy reaction‐diffusion equations

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

New Complex Hyperbolic Structures to the Lonngren-Wave Equation by Using Sine-Gordon Expansion Method

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