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Two efficient methods for solving Schlömilch’s integral equation
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Purpose

In this paper, the exact solutions of the Schlömilch’s integral equation and its linear and non-linear generalized formulas with application are solved by using two efficient iterative methods. The Schlömilch’s integral equations have many applications in atmospheric, terrestrial physics and ionospheric problems. They describe the density profile of electrons from the ionospheric for awry occurrence of the quasi-transverse approximations. The paper aims to discuss these issues.

Design/methodology/approach

First, the authors apply a regularization method combined with the standard homotopy analysis method to find the exact solutions for all forms of the Schlömilch’s integral equation. Second, the authors implement the regularization method with the variational iteration method for the same purpose. The effectiveness of the regularization-Homotopy method and the regularization-variational method is shown by using them for several illustrative examples, which have been solved by other authors using the so-called regularization-Adomian method.

Findings

The implementation of the two methods demonstrates the usefulness in finding exact solutions.

Practical implications

The authors have applied the developed methodology to the solution of the Rayleigh equation, which is an important equation in fluid dynamics and has a variety of applications in different fields of science and engineering. These include the analysis of batch distillation in chemistry, scattering of electromagnetic waves in physics, isotopic data in contaminant hydrogeology and others.

Originality/value

In this paper, two reliable methods have been implemented to solve several examples, where those examples represent the main types of the Schlömilch’s integral models. Each method has been accompanied with the use of the regularization method. This process constructs an efficient dealing to get the exact solutions of the linear and non-linear Schlömilch’s integral equation which is easy to implement. In addition to that, the accompanied regularization method with each of the two used methods proved its efficiency in handling many problems especially ill-posed problems, such as the Fredholm integral equation of the first kind.

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Publication Date
Tue Oct 01 2024
Journal Name
Renewable And Sustainable Energy Reviews
A critical review on the efficient cooling strategy of batteries of electric vehicles: Advances, challenges, future perspectives
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Publication Date
Tue Feb 01 2022
Journal Name
Baghdad Science Journal
Solving Whitham-Broer-Kaup-Like Equations Numerically by using Hybrid Differential Transform Method and Finite Differences Method
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This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

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Publication Date
Wed Jan 10 2024
Journal Name
The American Journal Of Interdisciplinary Innovation And Research
SUBJECT: REVIEW METHODS OF DETECTING SUGAR IN A SAMPLE
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Publication Date
Mon Jul 01 2019
Journal Name
J. Pharm. Sci. & Res.
Methods of Synthesis Phthalimide Derivatives and Biological Activity-Review
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Phthalimide formation of Phthalic anhydride with various amines using microwave or without a method with the difference of the catalyst used in a prepared Phthalimide, either structure general are C6H4CONRCO and used as starting materials in synthesis several compounds derivative phthalimides are an important compounds because spectrum wide biological activities including Antimicrobial activity, anticonvulsant activity, Anti-inflammatory activity,Analgesic activity, Anti- influenza activity and Thromboxane inhibitory activity

Publication Date
Mon Feb 01 2016
Journal Name
Journal Of Economics And Administrative Sciences
Operations Rescheduling Strategies, Policies, and Methods: A Philosophic Approach
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When scheduling rules become incapable to tackle the presence of a variety of unexpected disruptions frequently occurred in manufacturing systems,  it is necessary to develop a reactive schedule which can absorb the effects of such disruptions. Such responding requires efficient strategies, policies, and methods to controlling production & maintaining high shop performance. This can be achieved through rescheduling task which defined as an essential operating function to efficiently tackle and response to uncertainties and unexpected events. The framework proposed in this study consists of rescheduling approaches, strategies, policies, and techniques, which represents a guideline for most manufacturing companies operatin

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Publication Date
Sun Dec 03 2017
Journal Name
Baghdad Science Journal
Revaluation of Student Failure Reasons Using Non-Additive Methods
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In this paper, An application of non-additive measures for re-evaluating the degree of importance of some student failure reasons has been discussed. We apply non-additive fuzzy integral model (Sugeno, Shilkret and Choquet) integrals for some expected factors which effect student examination performance for different students' cases.

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Publication Date
Sun Apr 14 2019
Journal Name
Political Sciences Journal
Characterization of terrorist methods and how to address them
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توصيف الاساليب الارهابية وسبل مواجهتها

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Publication Date
Wed Jun 27 2018
Journal Name
Iraqi Journal Of Chemical And Petroleum Engineering
Comparison of Petrophysical Properties Measurement Methods in Sandston Rocks
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This paper displays a survey about the laboratory routine core analysis study on ten sandstone core samples taken from Zubair Reservoir/West Quarna Oil Field. The Petrophysical properties of rock as porosity, permeability, grain's size, roundness and sorting, type of mineral and volumes of shales inside the samples were tested by many apparatus in the Petroleum Technology Department/ University of Technology such as OFITE BLP-530 Gas Porosimeter, PERG-200TM Gas Permeameter and liquid Permeameter, GeoSpec2 apparatus (NMR method), Scanning Electron Microscopy (SEM) and OFITE Spectral Gamma Ray Logger apparatus. By comparing all the results of porosity and permeability measured by these instruments, it is clear a significant vari

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Publication Date
Mon Feb 14 2022
Journal Name
Journal Of Educational And Psychological Researches
Methods of Achieving Mental Health from an Islamic Perspective
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The aim of the research is to identify the methods of achieving mental health from an Islamic perspective by using an analytical approach. The methods that were explained: strengthen the spiritual side to control the motives and emotion s overcome the whims of the soul, fear of God and treat mental illness from an Islamic point of view by recognizing self, assurance, foresight, learning and acquiring new trends. Conclusion: we can achieve mental health by optimism, not despair, the compatibility of the Muslim with himself and with others, Consistency, emotional balance, and patience in difficult situations. Islam has attributes that make an individual feels    psychological security. Thus, all these elements achiev

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Publication Date
Wed May 17 2023
Journal Name
Journal Of Engineering
Comparison of the Combining Methods Used In Space Diversity
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The basic concept of diversity; where two or more inputs at the receiver are used to get uncorrelated signals. The aim of this paper is an attempt to compare some possible combinations of diversity reception and MLSE detection techniques. Various diversity combining techniques can be distinguished: Equal Gain Combining (EGC), Maximal Ratio Combining (MRC), Selection Combining and Selection Switching Combining (SS).The simulation results shows that the MRC give better performance than the other types of combining (about 1 dB compare with EGC and 2.5~3 dB compare with selection and selection switching combining).

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