Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations

Li, Jianlin

doi:10.1016/j.cam.2008.09.007

Cited by 33 publications

(10 citation statements)

References 28 publications

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“…Ibrahim used a new iterative method for solving the mixed Volterra-Fredholm integral equations [6]. Wazwaz treated this problem by using the method of series solutions and the Adomian decomposition method [7]. In addition, Wang used the least square approximation method to solve this type of equations [8].…”

Section: Hasan and Sulaimanmentioning

confidence: 99%

Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Hasan

Sulaiman

2020

eijs

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In this paper, the homotopy perturbation method is presented for solving the second kind linear mixed Volterra-Fredholm integral equations. Then, Aitken method is used to accelerate the convergence. In this method, a series will be constructed whose sum is the solution of the considered integral equation. Convergence of the constructed series is discussed, and its proof is given; the error estimation is also obtained. For more illustration, the method is applied on several examples and programs, which are written in MATLAB (R2015a) to compute the results. The absolute errors are computed to clarify the efficiency of the method.

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Section: Hasan and Sulaimanmentioning

confidence: 99%

Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Hasan

Sulaiman

2020

eijs

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“…In the beginning of 1980, ADM was developed by Adomian [ 30 , 31 ] and Ismail et al [ 32 ] used to solve Burger's-Huxley and Burger's-Fisher equations. More applications of ADM are cited in [ 33 – 36 ]. The convergence of the ADM is discussed in [ 37 – 39 ].…”

Section: Introductionmentioning

confidence: 99%

Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method

Tapaswini

Chakraverty

2014

The Scientific World Journal

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This paper proposes a new technique based on double parametric form of fuzzy numbers to handle the uncertain vibration equation for very large membrane for different particular cases. Uncertainties present in the initial condition and the wave velocity of free vibration are modelled through Gaussian convex normalised fuzzy set. Using the single parametric form of fuzzy number, the original fuzzy vibration equation is converted first to an interval fuzzy vibration equation. Next this equation is transformed to crisp form by applying double parametric form of fuzzy numbers. Finally the same governing equation is solved by Adomian decomposition method (ADM) symbolically to obtain the uncertain bounds. The present methods are very simple and effective. Obtained results are depicted in terms of plots to show the efficiency and powerfulness of the present analysis. Results obtained by the methods with new techniques are compared with existing results in special cases.

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“…In recent years, much attention has been devoted to the development of several powerful and useful methods for finding exact analytical solutions of nonlinear differential equations. These methods include the powerful Lie group method [1], the sine-cosine method [2], the tanh method [3,4], the extended tanh-function method [5], the Backlund transformation method [6], the transformed rational function method [7], the ( / )-expansion method [8], the exponential function rational expansion method [9], and the Adomian's decomposition method [10].…”

Section: Introductionmentioning

confidence: 99%

Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

Aziz

Fatima

Khalique

et al. 2013

Mathematical Problems in Engineering

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The simplest equation method is employed to construct some new exact closed-form solutions of the general Prandtl's boundary layer equation for two-dimensional flow with vanishing or uniform mainstream velocity. We obtain solutions for the case when the simplest equation is the Bernoulli equation or the Riccati equation. Prandtl's boundary layer equation arises in the study of various physical models of fluid dynamics. Thus finding the exact solutions of this equation is of great importance and interest.

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Adomian’s decomposition method and homotopy perturbation method in solving nonlinear equations

Cited by 33 publications

References 28 publications

Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Homotopy Perturbation Method and Convergence Analysis for the Linear Mixed Volterra-Fredholm Integral Equations

Non-probabilistic Solution of Uncertain Vibration Equation of Large Membranes Using Adomian Decomposition Method

Prandtl's Boundary Layer Equation for Two-Dimensional Flow: Exact Solutions via the Simplest Equation Method

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