Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory

Khan, Junaid Ali; Raja, Muhammad Asif Zahoor; Rashidi, Majid; Syam, Muhammed I.; Wazwaz, Abdul‐Majid

doi:10.1080/09540091.2015.1092499

Cited by 103 publications

(33 citation statements)

References 41 publications

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“…However, ANN based methodologies are widely used now a days in different fields of engineering and technology. Khan et al (2015) used nature inspired computing approach for solving non-linear problem arising in electromagnetic theory. Raja et al (2016) used bio-inspired computing technique in the field of nanotechnology.…”

Section: Nomenclaturementioning

confidence: 99%

Discharge coefficient of oblique sharp crested weir for free and submerged flow using trained ANN model

Ayaz

Mansoor

2018

Water Science

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In the present study, ANN models have been developed to predict the discharge coefficients of oblique sharp-crested weirs for free and submerged flow cases using Borghei et al.'s experimental data. The discharge coefficients predicted by ANN models are then used to predict the discharges. The results so obtained are compared with the traditional regression model analysis performed by Borghei et al. (2003) in which the prediction error in the discharge was found within the range of ±5%. On the other hand, the developed ANN models predict the discharge coefficients as well as discharges within the error range of ±1%. Furthermore, sensitivity analysis of developed ANN models have been carried out for all the parameters (weir height, oblique weir length, head over weir and downstream head over weir) involved in the study and it was found that the weir length (L) is the most and weir height (P) is the least sensitive input variable to ANN-1 model. In the case of ANN-2 model, weir length (L) is the most and downstream head over weir (H d) is the least sensitive input variable.

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Section: Nomenclaturementioning

confidence: 99%

Discharge coefficient of oblique sharp crested weir for free and submerged flow using trained ANN model

Ayaz

Mansoor

2018

Water Science

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“…However, artificial intelligence (AI) techniques have been largely used for finding the solution of initial value problems (IVPs) as well as boundary value problems (BVPs) of both linear and nonlinear type of differential equations [30][31][32][33]. Few recent applications in this domain are stochastic numerical of nonlinear Jeffery-Hamel flow study in the presence of high magnetic field [34], problems arising in electromagnetic theory [35], modelling of electrical conducting solids [36], fuel ignition type model working in combustion theory [37], magnetohydrodynamics (MHD) studies [38], fluid mechanics problems [39], drainage problem [40], plasma physics problems [41], Bratu's problems [42], Van-der-Pol oscillatory problems [43], Troesch's problems [44], nanofluidic problems [45], multiwalled carbon nanotubes studies [46], nonlinear Painleve systems [47], nonlinear pantograph systems [48] and nonlinear singular systems [49][50][51][52][53]. Furthermore, the extended form of these methods has been applied to compute the solution of linear and nonlinear well-known fractional differential equations [54,55].…”

Section: Introductionmentioning

confidence: 99%

Neural network methods to solve the Lane–Emden type equations arising in thermodynamic studies of the spherical gas cloud model

Ahmad

Raja

Bilal

et al. 2016

Neural Comput & Applic

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109

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In the present study, stochastic numerical computing approach is developed by applying artificial neural networks (ANNs) to compute the solution of Lane-Emden type boundary value problems arising in thermodynamic studies of the spherical gas cloud model. ANNs are used in an unsupervised manner to construct the energy function of the system model. Strength of efficient local optimization procedures based on active-set (AS), interior-point (IP) and sequential quadratic programming (SQP) algorithms is used to optimize the energy functions. The performance of all three design methodologies ANN-AS, ANN-IP and ANN-SQP is evaluated on different nonlinear singular systems. The effectiveness of the proposed schemes in terms of accuracy and convergence is established from the results of statistical indicators.

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“…Many facts have proved that the adaptability of the two models are poor because they are rigorous homogenous exponent with the inflexible model structure. To solve this problem, Zeng bo proposed a self‐adaptive intelligence gray predictive model with an alterable structure, SAIGM for short. The proposed SAIGM model has the advantages of adjustable parameters and is characterized by its variable structure as a homogenous or nonhomogenous exponent model or as a single‐variable linear‐autoregression model.…”

Section: Introductionmentioning

confidence: 99%

A self‐adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application

Zeng

Liu

2017

Math Methods in App Sciences

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The self-adaptive intelligence gray predictive model (SAIGM) has an alterableflexible model structure, and it can build a dynamic structure to fit different external environments by adjusting the parameter values of SAIGM. However, the order number of the raw SAIGM model is not optimal, which is an integer. For this, a new SAIGM model with the fractional order accumulating operator (SAIGM_FO) was proposed in this paper. Specifically, the final restored expression of SAIGM_FO was deduced in detail, and the parameter estimation method of SAIGM_FO was studied. After that, the Particle Swarm Optimization algorithm was used to optimize the order number of SAIGM_FO, and some steps were provided. Finally, the SAIGM_FO model was applied to simulate China's electricity consumption from 2001 to 2008 and forecast it during 2009 to 2015, and the mean relative simulation and prediction percentage errors of the new model were only 0.860% and 2.661%, in comparison with the ones obtained from the raw SAIGM model, the GM(1, 1) model with the optimal fractional order accumulating operator and the GM(1, 1) model, which were (1.201%, 5.321%), (1.356%, 3.324%), and (2.013%, 23.944%), respectively. The findings showed both the simulation and the prediction performance of the proposed SAIGM_FO model were the best among the 4 models.KEYWORDS fractional order accumulating operator, particle swarm optimization algorithm, prediction of China's electricity consumption, self-adaptive intelligence gray predictive model | INTRODUCTIONThe importance of prediction for management decision making is self-evident. With the development of science and technology, various prediction methods have been emerged. Thereinto, regression prediction model and gray prediction model 1 are two kind of frequently used prediction methods. The major difference between them is the different sample size for modeling: The former needs only a little sample data (not less than 4), and the latter is built based on large sample data (the sample size should be greater than 30). However, for some applications, it is very difficult to obtain the large sample data. For example, holing and sampling are an important means to analyze the oil and gas reserves of some region; however, the cost of holing is too high to drill many holes. Hence, we cannot obtain the large sample data about

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Nature-inspired computing approach for solving non-linear singular Emden–Fowler problem arising in electromagnetic theory

Cited by 103 publications

References 41 publications

Discharge coefficient of oblique sharp crested weir for free and submerged flow using trained ANN model

Discharge coefficient of oblique sharp crested weir for free and submerged flow using trained ANN model

Neural network methods to solve the Lane–Emden type equations arising in thermodynamic studies of the spherical gas cloud model

A self‐adaptive intelligence gray prediction model with the optimal fractional order accumulating operator and its application

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