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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
Sun May 07 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Development Of Two Different Spectrophotometric Methods For The Determination Of Atropine Drug In Pure Form And Pharmaceutical Preparations
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Two methods have been applied for the spectrophotometric determination of atropine, in
bulk sample and in dosage form. The methods are accurate, simple, rapid, inexpensive and
sensitive. The first method depending on the extraction of the formed ion-pair complex with
bromphenol blue (BPB) as a chromogenic reagent in chloroform, use phthalate buffer of pH
3.0; which showed absorbance maxima at 413 nm against reagent blank. The calibration
graph is linear in the ranges of 0.5-40 µg.mL
-1
with detection limit of 0.363µg.mL
-1
. The
second method depending on the measure of the absorbance maxima of the formed charge-transfer complex with 2,3-dichloro-5,6-dicyano-p-benzoquinone (DDQ) at 457 nm against

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Publication Date
Sun Mar 18 2018
Journal Name
Https://www.iasj.net/iasj/article/170012#:~:text=al.qadisiya%20journal%20for%20the%20sciences%20of%20physical%20education
The Effect Of Using Two Strategies For Active Learning ( Jigsaw Strategy & Problems Solving) In Learning Some Balanced Beam's Skills In Artistic Gymnastics
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The aim of this study to identify the effect of using two strategies for active learning ( Jigsaw Strategy & Problems Solving) in learning some balanced beam's skills in artistic gymnastics for women , as well as to identify the best of the three methods (jigsaw strategy , problems solving and the traditional method) in learning some skills balance beam , the research has used the experimental methodology, and the subject included the students of the college of Physical Education and Sports Sciences / University of Baghdad / third grade and by the lot was selected (10) students for each group of groups Search three and The statistical package for social sciences (SPSS) was used means, the standard deviation and the (T.test), the one way a n

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Publication Date
Sun Jun 04 2017
Journal Name
Baghdad Science Journal
Studying the Electron Energy Distribution Function (EEDF) and Electron Transport Coefficients in SF6 – He Gas Mixtures by Solving the Boltzmann Equation
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The Boltzmann equation has been solved using (EEDF) package for a pure sulfur hexafluoride (SF6) gas and its mixtures with buffer Helium (He) gas to study the electron energy distribution function EEDF and then the corresponding transport coefficients for various ratios of SF6 and the mixtures. The calculations are graphically represented and discussed for the sake of comparison between the various mixtures. It is found that the various SF6 – He content mixtures have a considerable effect on EEDF and the transport coefficients of the mixtures

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Publication Date
Sun Jun 12 2011
Journal Name
Baghdad Science Journal
Satellite Images Unsupervised Classification Using Two Methods Fast Otsu and K-means
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Two unsupervised classifiers for optimum multithreshold are presented; fast Otsu and k-means. The unparametric methods produce an efficient procedure to separate the regions (classes) by select optimum levels, either on the gray levels of image histogram (as Otsu classifier), or on the gray levels of image intensities(as k-mean classifier), which are represent threshold values of the classes. In order to compare between the experimental results of these classifiers, the computation time is recorded and the needed iterations for k-means classifier to converge with optimum classes centers. The variation in the recorded computation time for k-means classifier is discussed.

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Crossref
Publication Date
Sun Dec 07 2014
Journal Name
Baghdad Science Journal
Baysian and NonBaysian Methods to Estimate the two parameters of Logistic Distribution
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In this paper ,the problem of point estimation for the two parameters of logistic distribution has been investigated using simulation technique. The rank sampling set estimator method which is one of the Non_Baysian procedure and Lindley approximation estimator method which is one of the Baysian method were used to estimate the parameters of logistic distribution. Comparing between these two mentioned methods by employing mean square error measure and mean absolute percentage error measure .At last simulation technique used to generate many number of samples sizes to compare between these methods.

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Crossref (1)
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Publication Date
Tue Dec 03 2013
Journal Name
Baghdad Science Journal
Satellite Images Unsupervised Classification Using Two Methods Fast Otsu and K-means
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Publication Date
Mon May 20 2019
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
New Technique for Solving Autonomous Equations
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This paper demonstrates a new technique based on a combined form of the new transform method with homotopy perturbation method to find the suitable accurate solution of autonomous Equations with initial condition.  This technique is called the transform homotopy perturbation method (THPM). It can be used to solve the problems without resorting to the frequency domain.The implementation of the suggested method demonstrates the usefulness in finding exact solution for linear and nonlinear problems. The practical results show the efficiency and reliability of technique and easier implemented than HPM in finding exact solutions.Finally, all algorithms in this paper implemented in MATLAB version 7.12.

 

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Crossref (3)
Crossref
Publication Date
Fri Jul 28 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Development of Two New Spectrophotometeric Methods for the Determination of Amitriptyline in Pharmaceutical Preparation Using Univariate and Simplex Optimization
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 Two simple and sensitive spectrophotometric methods are proposed for the determination of amitriptyline in its pure form and in tablets. The first method is based on the formation of charge- transfer complex between amitriptyline as n-donor and tetracyano-ethylene (TCNE) as Ï€acceptor. The product exhibit absorbance maximum at 470 nm in acetonitrile solvent (pH =9.0 ) . In the second method the absorbance of the ion- pair complex, which is formed between the soughted drug and bromocresol green (BCG), was measured at 415 nm at ( pH=3.5) . In addition to classical univariate optimization, modified simplex method (MSM) was applied in the optimization of the variable affecting  the color producing reaction by a geometric simple

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Publication Date
Sun Jun 01 2014
Journal Name
Baghdad Science Journal
Using Bernoulli Equation to Solve Burger's Equation
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In this paper we find the exact solution of Burger's equation after reducing it to Bernoulli equation. We compare this solution with that given by Kaya where he used Adomian decomposition method, the solution given by chakrone where he used the Variation iteration method (VIM)and the solution given by Eq(5)in the paper of M. Javidi. We notice that our solution is better than their solutions.

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Crossref
Publication Date
Tue Jan 01 2019
Journal Name
Malaysian Journal Of Biochemistry And Molecular Biology
Efficiency of primer design tools in evaluation of two molecular methods to detect two single nucleotide polymorphisms related with atherosclerosis
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