Solution of different geometries reflected reactors neutron diffusion equation using the homotopy perturbation method

Shqair, Mohammed

doi:10.1016/j.rinp.2018.11.025

Cited by 31 publications

(7 citation statements)

References 17 publications

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“…Nonlinear oscillations arise everywhere in our everyday life and engineering. As an exact solution might be too complex to be used for a practical application, many analytical methods have been used in open literature, for example, the variational iteration method, [1][2][3][4][5][6][7] the homotopy perturbation method, [8][9][10][11][12][13][14][15][16][17][18][19][20] He-Laplace method, [21][22][23] the variational approach [24][25][26][27][28][29] and the Hamiltonian approach. 30,31 The most important property of a nonlinear oscillator is the relationship between the frequency and its amplitude, the simplest method to estimate the frequency-amplitude relationship might be He's frequency formulation [32][33][34] and the max-min approach, 35,36 which are still under development and many modifications were proposed to improve the accuracy.…”

Section: Introductionmentioning

confidence: 99%

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

2019

Journal of Low Frequency Noise, Vibration and Active Control

190

105

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In engineering, a fast estimation of the periodic property of a nonlinear oscillator is much needed. This paper reviews some simplest methods for nonlinear oscillators, including He's frequency formulation, the max-min approach and the homotopy perturbation method. A mathematical insight into He's frequency formulation is given, and the weighted average is introduced to further improve the estimated accuracy of the frequency. Fractional oscillators are also discussed.

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Section: Introductionmentioning

confidence: 99%

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

2019

Journal of Low Frequency Noise, Vibration and Active Control

190

105

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“…Couple boundary conditions are considered in such a way diffusion flux vanishes at the critical dimension. As in the same procedure that used in previous works like [20,21], one of the fluxes is normalized (to one) at the core of the reactor, and the other fluxes will be calculated depending on Equation 5as ratios of the normalized flux, for two energy groups of neutrons the ratio between thermal and fast fluxes is given in the data source [2] which convenient with Equation (5) calculations.…”

Section: Practical Numerical Resultsmentioning

confidence: 99%

“…An alternative method is used to solve one energy group of a neutron diffusion equation in cylindrical symmetry [16]. There are other efforts to solve different cases of neutron diffusion equations [17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

2019

Self Cite

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In this paper, a multi-energy groups of a neutron diffusion equations system is analytically solved by a residual power series method. The solution is generalized to consider three different geometries: slab, cylinder and sphere. Diffusion of two and four energy groups of neutrons is specifically analyzed through numerical calculation at certain boundary conditions. This study revels sufficient analytical description for radial flux distribution of multi-energy groups of neutron diffusion theory as well as determination of each nuclear reactor dimension in criticality case. The generated results are compatible with other different methods data. The generated results are practically efficient for neutron reactors dimension.

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“…When applied to Volterra's integro-differential equation, HPM did not require small parameters in the equations, which may eliminate the limitations of the standard perturbation methods [44]. It was also found that HPM was applied in a direct way without using linearization, transformation, discretization or restrictive assumptions [8,14,17,18,43,55,65,74].…”

Section: The Performance Of the Application Of The Hpmmentioning

confidence: 99%

The Application of Homotopy Perturbation Method: An Overview

Yang

2022

ARJOM

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As an effective method for solving linear and nonlinear equations, the homotopy perturbation method is usually applied to solving relevant problems. We analyze 74 studies on the application of the homotopy perturbation method and present a comprehensive review of them with the conclusion obtained: (1) Homotopy perturbation method is generally applied to solving the problems of ordinary differential equations; (2) Homotopy perturbation method is usually combined with the technology of transform when it is used to solve more complicated equations; (3) By comparing homotopy perturbation method with other similar methods, many researchers sought that homotopy perturbation method is rapidly convergent, highly accurate, computational simple; (4) Some studies point out that when homotopy perturbation method is applied, some parameters including the number of terms, time span, time step must be prescribed carefully. Finally, two suggestions on the further study of the application of the HPM are provided.

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Solution of different geometries reflected reactors neutron diffusion equation using the homotopy perturbation method

Cited by 31 publications

References 17 publications

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

The simpler, the better: Analytical methods for nonlinear oscillators and fractional oscillators

Analytical Solution for Multi-Energy Groups of Neutron Diffusion Equations by a Residual Power Series Method

The Application of Homotopy Perturbation Method: An Overview

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