An advanced study on the solution of nanofluid flow problems via Adomian’s method

Ebaid, Abdelhalim; Aljoufi, Mona D.; Wazwaz, Abdul‐Majid

doi:10.1016/j.aml.2015.02.017

Cited by 31 publications

(17 citation statements)

References 18 publications

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“…In order to overcome such drawback, a new series solution shall be deduced by using the Adomian decomposition method (ADM) which possesses more accuracy and validity. The ADM was applied to solving algebraic/transcendental/matrix equations [5][6][7][8][9], besides nonlinear integral/differential equations and both IVPs/BVPs, even for irregular boundary contours [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The solution of this method is an infinite series which converges when choosing an appropriate canonical form.…”

Section: Introductionmentioning

confidence: 99%

Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

Ebaid

Al-Enazi

Albalawi

et al. 2019

MCA

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The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

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Section: Introductionmentioning

confidence: 99%

Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

Ebaid

Al-Enazi

Albalawi

et al. 2019

MCA

Self Cite

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“…However, the conformable derivative (CD) is one of the most prominent operators in this context. To solve the generalized model (Equations (1) and (2)) using the CD, several analytical approaches can be implemented such as the Adomian decomposition method (ADM) [8][9][10][11][12][13][14][15][16][17][18][19][20], the homotopy perturbation method (HPM) [21][22][23], the differential transform method (DTM)/Taylor expansion [24,25], and the the homotopy analysis method (HAM) [6]. In addition, many applications of the CD have been recently discussed by several authors [26][27][28][29].…”

Section: Introductionmentioning

confidence: 99%

Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

2019

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This paper addresses the modelling of Ambartsumian equation using the conformable derivative as an application of the theory of surface brightness in astronomy. The homotopy perturbationmethod is applied to solve this model, where the approximate solution is given in terms of the conformable derivative order and the exponential functions. The present solution reduces to the corresponding one in the relevant literature as a special case. Moreover, a rapid rate of convergence has been achieved for the obtained approximate solutions. Furthermore, the accuracy of the obtained numerical results is validated via calculating the residual against the impeded parameters. It is shown graphically that the obtained residual approaches zero in various cases, which proves the efficiency of the current analysis.

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“…The ADM was applied to solving algebraic/transcendental/matrix equations [5][6][7][8][9], nonlinear integral/differential equations and both of initial and boundary value problems (IVPs/BVPs), even for irregular boundary contours [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24]. The solution for this method is an infinite series, which converges when choosing an appropriate canonical form.…”

Section: Introductionmentioning

confidence: 99%

Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

Bakodah

Ebaid

2018

Mathematics

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The Ambartsumian equation, a linear differential equation involving a proportional delay term, is used in the theory of surface brightness in the Milky Way. In this paper, the Laplace-transform was first applied to this equation, and then the decomposition method was implemented to establish a closed-form solution. The present closed-form solution is reported for the first time for the Ambartsumian equation. Numerically, the calculations have demonstrated a rapid rate of convergence of the obtained approximate solutions, which are displayed in several graphs. It has also been shown that only a few terms of the new approximate solution were sufficient to achieve extremely accurate numerical results. Furthermore, comparisons of the present results with the existing methods in the literature were introduced.

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An advanced study on the solution of nanofluid flow problems via Adomian’s method

Cited by 31 publications

References 18 publications

Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

Solution of Ambartsumian Delay Differential Equation with Conformable Derivative

Exact Solution of Ambartsumian Delay Differential Equation and Comparison with Daftardar-Gejji and Jafari Approximate Method

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