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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
Fri Apr 28 2023
Journal Name
Mathematical Modelling Of Engineering Problems
Design Optimal Neural Network for Solving Unsteady State Confined Aquifer Problem
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Publication Date
Mon Dec 04 2023
Journal Name
Aip Conf. Proc
Double LA-transform and their properties for solving partial differential equations
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Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Application of Iterative Method for Solving Higher Order Integro-Differential Equations
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The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

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Publication Date
Tue Oct 16 2018
Journal Name
Springer Science And Business Media Llc
MOGSABAT: a metaheuristic hybrid algorithm for solving multi-objective optimisation problems
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Publication Date
Sat Jun 12 2021
Journal Name
2021 International Conference On Electrical, Communication, And Computer Engineering (icecce)
Efficient Private Cloud Resources Platform
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Publication Date
Mon Jun 10 2024
Journal Name
Iraqi Journal For Computer Science And Mathematics
Solving tri-criteria: total completion time, total late work, and maximum earliness by using exact, and heuristic methods on single machine scheduling problem
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The presented study investigated the scheduling regarding  jobs on a single machine. Each  job will be processed with no interruptions and becomes available for the processing at time 0. The aim is finding a processing order with regard to jobs, minimizing total completion time , total late work , and maximal tardiness  which is an NP-hard problem. In the theoretical part of the present work, the mathematical formula for the examined problem will be presented, and a sub-problem of the original problem of minimizing the multi-objective functions  is introduced. Also, then the importance regarding the dominance rule (DR) that could be applied to the problem to improve good solutions will be shown. While in the practical part, two

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Publication Date
Sat Sep 23 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
An Efficient S.brunken Estimators For The Mean Of Normal Population With Kuown Variance
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This  article  co;nsiders a shrunken  estimator  Â·Of  Al-Hermyari·   and

AI Gobuii (.1) to estimate  the mean (8) of a normal clistributicm N (8 cr4)  with  known variance  (cr+),  when  <:I    guess value (So) av11il ble about the mean (B) as· an initial estrmate. This estimator is shown to be

more efficient tl1an the class-ical estimators  especially when 8 is close to 8•. General expressions .for bias and MSE -of considered  estitnator are gi 'en, witeh  some examples.  Nut.nerical cresdlts, comparisons  and

conclusions ate reported.

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Publication Date
Sun Mar 05 2017
Journal Name
Baghdad Science Journal
An efficient of Sansevieriatrifasciataplantas biosorbent for the treatment of metal contaminated industrial effluents
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Sansevieriatrifasciata was studied as a potential biosorbent for chromium, copper and nickel removal in batch process from electroplating and tannery effluents. Different parameters influencing the biosorption process such as pH, contact time, and amount of biosorbent were optimized while using the 80 mm sized particles of the biosorbent. As high as 91.3 % Ni and 92.7 % Cu were removed at pH of 6 and 4.5 respectively, while optimum Cr removal of 91.34 % from electroplating and 94.6 % from tannery effluents was found at pH 6.0 and 4.0 respectively. Pseudo second order model was found to best fit the kinetic data for all the metals as evidenced by their greater R2 values. FTIR characterization of biosorbent revealed the presence of carboxyl a

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Publication Date
Mon Apr 01 2019
Journal Name
2019 International Conference On Automation, Computational And Technology Management (icactm)
Multi-Resolution Hierarchical Structure for Efficient Data Aggregation and Mining of Big Data
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Big data analysis is essential for modern applications in areas such as healthcare, assistive technology, intelligent transportation, environment and climate monitoring. Traditional algorithms in data mining and machine learning do not scale well with data size. Mining and learning from big data need time and memory efficient techniques, albeit the cost of possible loss in accuracy. We have developed a data aggregation structure to summarize data with large number of instances and data generated from multiple data sources. Data are aggregated at multiple resolutions and resolution provides a trade-off between efficiency and accuracy. The structure is built once, updated incrementally, and serves as a common data input for multiple mining an

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Publication Date
Sat Jul 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Polyacrylonitrile Nanofiber Composites as Efficient Removal of Pollutants for Wastewater: A Review Article
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Polyacrylonitrile nanofiber (PANFS), a well-known polymers, has been extensively employed in the manufacturing of carbon nanofibers (CNFS), which have recently gained substantial attention due to their excellent features, such as spinnability, environmental friendliness, and commercial feasibility. Because of their high carbon yield and versatility in tailoring the final CNFS structure, In addition to the simple formation of ladder structures through nitrile polymerization to yield stable products, CNFS and PAN have been the focus of extensive research as potential production precursors. For instance, the development of biomedical and high-performance composites has now become achievable. PAN homopolymer or PAN-based precursor copolymer can

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