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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 Jan 28 2020
Journal Name
Journal Of Accounting And Financial Studies ( Jafs )
Forecasting the performance and profitability of companies using the equation of Tobin’sq
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The main objective and primary concern to every investor not only to achieve a greater return on his or her investments, but also to create the largest possible value of these investments the, researchers and those interested in the field of investment and financial analysis  try to develop standards  for performance      valuation      is guided through the                                     &nbsp

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Publication Date
Tue Dec 01 2020
Journal Name
Baghdad Science Journal
Numerical Solution of Fractional Volterra-Fredholm Integro-Differential Equation Using Lagrange Polynomials
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In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

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Publication Date
Fri Jan 01 2016
Journal Name
مجلة المستنصرية للعلوم والتربية
Calculation of Electron Drift Velocity in Xenon Gas Using Boltzmann Equation Analysis
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Publication Date
Tue Jun 20 2023
Journal Name
Baghdad Science Journal
Delay differential equation of the 2nd order and it's an oscillation yardstick
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This study focuses on studying an oscillation of a second-order delay differential equation. Start work, the equation is introduced here with adequate provisions. All the previous is braced by theorems and examplesthat interpret the applicability and the firmness of the acquired provisions

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Scopus Crossref
Publication Date
Tue May 01 2018
Journal Name
Journal Of Physics: Conference Series
The Approximate Solution of Fractional Damped Burger’s Equation and its Statistical Properties
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Publication Date
Fri Apr 01 2016
Journal Name
Communications In Nonlinear Science And Numerical Simulation
Simultaneous determination of time and space-dependent coefficients in a parabolic equation
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Scopus (23)
Crossref (13)
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Publication Date
Sat Jun 01 2013
Journal Name
Journal Of Economics And Administrative Sciences
Comparison between some well- Known methods to estimate the parameter of the proposed method of measurement and the reliability of the distribution function with two parameters Rally by simulation
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Abstract

            Rayleigh distribution is one of the important distributions used for analysis life time data, and has applications in reliability study and physical interpretations. This paper introduces four different methods to estimate the scale parameter, and also estimate reliability function; these methods are Maximum Likelihood, and Bayes and Modified Bayes, and Minimax estimator under squared error loss function, for the scale and reliability function of the generalized Rayleigh distribution are obtained. The comparison is done through simulation procedure, t

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Publication Date
Thu Apr 01 2021
Journal Name
Complexity
Bayesian Regularized Neural Network Model Development for Predicting Daily Rainfall from Sea Level Pressure Data: Investigation on Solving Complex Hydrology Problem
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Prediction of daily rainfall is important for flood forecasting, reservoir operation, and many other hydrological applications. The artificial intelligence (AI) algorithm is generally used for stochastic forecasting rainfall which is not capable to simulate unseen extreme rainfall events which become common due to climate change. A new model is developed in this study for prediction of daily rainfall for different lead times based on sea level pressure (SLP) which is physically related to rainfall on land and thus able to predict unseen rainfall events. Daily rainfall of east coast of Peninsular Malaysia (PM) was predicted using SLP data over the climate domain. Five advanced AI algorithms such as extreme learning machine (ELM), Bay

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Scopus (23)
Crossref (17)
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Publication Date
Sun May 01 2016
Journal Name
Iraqi Journal Of Science
Efficient text in image hiding method based on LSB method principle
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The steganography (text in image hiding) methods still considered important issues to the researchers at the present time. The steganography methods were varied in its hiding styles from a simple to complex techniques that are resistant to potential attacks. In current research the attack on the host's secret text problem didn’t considered, but an improved text hiding within the image have highly confidential was proposed and implemented companied with a strong password method, so as to ensure no change will be made in the pixel values of the host image after text hiding. The phrase “highly confidential” denoted to the low suspicious it has been performed may be found in the covered image. The Experimental results show that the covere

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Publication Date
Thu Nov 08 2018
Journal Name
Iraqi National Journal Of Nursing Specialties
Effect of using two packing Technic on Hardness of two dental acrylic resin
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Objective: the aim of this study is to invest age and determine the effect of using (2) packing
technique (conventional and new tension technique) on hardness of (2) types of heat cure acrylic
resin which are (Ivoclar and Qual dental type).
Methodology : this study was intended the using of two types of heat cure acrylic (IVoclar and
Qual dental type) which are used in construction of complete denture which packed in two different
packing technique (conventional and new tension technique) and accomplished by using a total of
(40) specimens in diameter of ( 2mm thickness, 2 cm length and 1 cm width) . This specimens were
sectioned and subdivide into (4) group each (10) specimens for one group , then signed as (A, Al B

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