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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
Sat Nov 12 2016
Journal Name
International Journal Of Mechanical Engineering And Technology (ijmet)
PERFORMANCE OF TWO-WAY NESTING TECHNIQUES FOR SHALLOW WATER MODELS
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A new two-way nesting technique is presented for a multiple nested-grid ocean modelling system. The new technique uses explicit center finite difference and leapfrog schemes to exchange information between the different subcomponents of the nested-grid system. The performance of the different nesting techniques is compared, using two independent nested-grid modelling systems. In this paper, a new nesting algorithm is described and some preliminary results are demonstrated. The validity of the nesting method is shown in some problems for the depth averaged of 2D linear shallow water equation.

Publication Date
Thu Jun 01 2023
Journal Name
Journal Of Engineering
Evaluating Roads Network Connectivity for Two Municipalities in Baghdad-Iraq
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The road network serves as a hub for opportunities in production and consumption, resource extraction, and social cohabitation. In turn, this promotes a higher standard of living and the expansion of cities. This research explores the road network's spatial connectedness and its effects on travel and urban form in the Al-Kadhimiya and Al-Adhamiya municipalities. Satellite images and paper maps have been employed to extract information on the existing road network, including their kinds, conditions, density, and lengths. The spatial structure of the road network was then generated using the ArcGIS software environment. The road pattern connectivity was evaluated using graph theory indices. The study demands the abstraction and examin

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Publication Date
Tue Sep 01 2020
Journal Name
Al-khwarizmi Engineering Journal
Two-Stage Classification of Breast Tumor Biomarkers for Iraqi Women
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Objective: Breast cancer is regarded as a deadly disease in women causing lots of mortalities. Early diagnosis of breast cancer with appropriate tumor biomarkers may facilitate early treatment of the disease, thus reducing the mortality rate. The purpose of the current study is to improve early diagnosis of breast by proposing a two-stage classification of breast tumor biomarkers fora sample of Iraqi women.

Methods: In this study, a two-stage classification system is proposed and tested with four machine learning classifiers. In the first stage, breast features (demographic, blood and salivary-based attributes) are classified into normal or abnormal cases, while in the second stage the abnormal breast cases are

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Publication Date
Sat Dec 01 2012
Journal Name
Journal Of Economics And Administrative Sciences
A comparison Some of Methods for Estimating Survival Function for Truncated Exponential Distribution
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Exponential distribution is one of most common distributions in studies and scientific researches with wide application in the fields of reliability, engineering and in analyzing survival function therefore the researcher has carried on extended studies in the characteristics of this distribution.

In this research, estimation of survival function for truncated exponential distribution in the maximum likelihood  methods and Bayes first and second method, least square method and Jackknife dependent in the first place on the maximum likelihood method, then on Bayes first method then comparing then using simulation, thus to accomplish this task, different size samples have been adopted by the searcher us

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Publication Date
Sat Mar 04 2023
Journal Name
Baghdad Science Journal
Approximate Solution of Sub diffusion Bio heat Transfer Equation
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In this paper, author’s study sub diffusion bio heat transfer model and developed explicit finite difference scheme for time fractional sub diffusion bio heat transfer equation by using caputo fabrizio fractional derivative. Also discussed conditional stability and convergence of developed scheme. Furthermore numerical solution of time fractional sub diffusion bio heat transfer equation is obtained and it is represented graphically by Python.

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Publication Date
Fri Jan 01 2016
Journal Name
Pure And Applied Mathematics Journal
Memory Effects in Diffusion Like Equation Via Haar Wavelets
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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
On Solution of Min-Max Composition Fuzzy Relational Equation
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In this paper, Min-Max composition fuzzy relation equation are studied. This study is a generalization of the works of Ohsato and Sekigushi. The conditions for the existence of solutions are studied, then the resolution of equations is discussed.

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Publication Date
Sat Jun 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Using Some Robust Methods For Handling the Problem of Multicollinearity
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The multiple linear regression model is an important regression model that has attracted many researchers in different fields including applied mathematics, business, medicine, and social sciences , Linear regression models involving a large number of independent variables are poorly performing due to large variation and lead to inaccurate conclusions , One of the most important problems in the regression analysis is the multicollinearity Problem, which is considered one of the most important problems that has become known to many researchers  , As well as their effects on the multiple linear regression model, In addition to multicollinearity, the problem of outliers in data is one of the difficulties in constructing the reg

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Publication Date
Sun Sep 01 2024
Journal Name
Kufa Journal For Agricultural Sciences
Comparing Different laboratory Methods for Measuring the Feed Pellet Durability
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The experiment aimed to compare different methods of measuring the Feed pellet durability through the effect of pellet die speeds and the particle size (mill sieve holes diameter). Feed pellet durability was studied in four different ways: pellet direct measurement (%), pellet lengths (%), pellet water absorption (%), pellet durability by drop box device (%), pellet durability by air pressure device (%). Three pellet die speeds 280, 300, and 320 rpm, three mill sieve holes diameter 2, 4, and 6 mm, have been used. The results showed that increasing the pellet die speeds from 280 to 300 then to 320 rpm led to a significant decrease in the feed pellet durability by direct measurement, drop box device, and air pressure device, while pel

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Publication Date
Mon Feb 01 2021
Journal Name
Journal Of Physics: Conference Series
The Convergence of Iterative Methods for Quasi δ-Contraction Mappings
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Abstract<p>In this article, we will present a quasi-contraction mapping approach for D iteration, and we will prove that this iteration with modified SP iteration has the same convergence rate. At the other hand, we prove that the D iteration approach for quasi-contraction maps is faster than certain current leading iteration methods such as, Mann and Ishikawa. We are giving a numerical example, too.</p>
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