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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 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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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
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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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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Scopus (8)
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Publication Date
Thu Dec 01 2022
Journal Name
Bulletin Of Electrical Engineering And Informatics
A model for incorporating suitable methods of usability evaluation into agile software development
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The challenge to incorporate usability evaluation values and practices into agile development process is not only persisting but also systemic. Notable contributions of researchers have attempted to isolate and close the gaps between both fields, with the aim of developing usable software. Due to the current absence of a reference model that specifies where and how usability activities need to be considered in the agile development process. This paper proposes a model for identifying appropriate usability evaluation methods alongside the agile development process. By using this model, the development team can apply usability evaluations at the right time at the right place to get the necessary feedback from the end-user. Verificatio

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Publication Date
Thu Sep 30 2021
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of Some Methods for Estimating Mixture of Linear Regression Models with Application
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 A mixture model is used to model data that come from more than one component. In recent years, it became an effective tool in drawing inferences about the complex data that we might come across in real life. Moreover, it can represent a tremendous confirmatory tool in classification observations based on similarities amongst them. In this paper, several mixture regression-based methods were conducted under the assumption that the data come from a finite number of components. A comparison of these methods has been made according to their results in estimating component parameters. Also, observation membership has been inferred and assessed for these methods. The results showed that the flexible mixture model outperformed the others

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Crossref
Publication Date
Sun Dec 04 2011
Journal Name
Baghdad Science Journal
Quantitative and Qualitative detect for cheat beef with chicken meat by immunological methods
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beef and chicken meat were used to get Sarcoplasim, the chicken Sarcoplasim were used to prepare antibody for it after injected in rabbit, the antiserums activity were 1/32 by determined with Immune double diffusion test, the self test refer to abele for some antiserums to detected with beef sarcoplasim, which it mean found same proteins be between beef and chicken meat, which it refer to difficult depended on this immune method to detect for cheat of chicken meat with beef, so the antibody for beef sarcoplasim were removed from serum by immune absorption step to produce specific serum against chicken sarcoplasim that it used in Immune double diffusion test to qualitative detect for cheat beef with 5% chicken meat or more at least, and the

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Publication Date
Wed Jan 01 2025
Journal Name
Aip Conference Proceedings
Comparative analysis of parameter estimation methods for Meixner process using wavelet packet transform
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The current research creates an overall relative analysis concerning the estimation of Meixner process parameters via the wavelet packet transform. Of noteworthy presentation relevance, it compares the moment method and the wavelet packet estimator for the four parameters of the Meixner process. In this paper, the research focuses on finding the best threshold value using the square root log and modified square root log methods with the wavelet packets in the presence of noise to enhance the efficiency and effectiveness of the denoising process for the financial asset market signal. In this regard, a simulation study compares the performance of moment estimation and wavelet packets for different sample sizes. The results show that wavelet p

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Publication Date
Wed Jan 11 2023
Journal Name
Mathematical Problems In Engineering
Bayesian Methods for Estimation the Parameters of Finite Mixture of Inverse Rayleigh Distribution
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Methods of estimating statistical distribution have attracted many researchers when it comes to fitting a specific distribution to data. However, when the data belong to more than one component, a popular distribution cannot be fitted to such data. To tackle this issue, mixture models are fitted by choosing the correct number of components that represent the data. This can be obvious in lifetime processes that are involved in a wide range of engineering applications as well as biological systems. In this paper, we introduce an application of estimating a finite mixture of Inverse Rayleigh distribution by the use of the Bayesian framework when considering the model as Markov chain Monte Carlo (MCMC). We employed the Gibbs sampler and

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