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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 Jan 01 2011
Journal Name
International Journal Of Computer Theory And Engineering
MIPOG - An Efficient t-Way Minimization Strategy for Combinatorial Testing
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Publication Date
Tue Jan 01 2008
Journal Name
Lecture Notes In Computer Science
IRPS – An Efficient Test Data Generation Strategy for Pairwise Testing
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Publication Date
Sat Jan 01 2022
Journal Name
Webology
Efficient Eye Recognition for Secure Systems Using Convolutional Neural Network
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AA Abbass, HL Hussein, WA Shukur, J Kaabi, R Tornai, Webology, 2022 Individual’s eye recognition is an important issue in applications such as security systems, credit card control and guilty identification. Using video images cause to destroy the limitation of fixed images and to be able to receive users’ image under any condition as well as doing the eye recognition. There are some challenges in these systems; changes of individual gestures, changes of light, face coverage, low quality of video images and changes of personal characteristics in each frame. There is a need for two phases in order to do the eye recognition using images; revelation and eye recognition which will use in the security systems to identify the persons. The mai

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Publication Date
Tue Feb 01 2022
Journal Name
Webology
Efficient Eye Recognition for Secure Systems using Convolutional Neural Network
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Publication Date
Tue Mar 30 2021
Journal Name
Baghdad Science Journal
Solvability of Some Types for Multi-fractional Integro-Partial Differential Equation
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In this article, the solvability of some proposal types of the multi-fractional integro-partial differential system has been discussed in details by using the concept of abstract Cauchy problem and certain semigroup operators and some necessary and sufficient conditions. 

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Publication Date
Tue Jun 01 2021
Journal Name
Baghdad Science Journal
Numerical Solution for Linear Fredholm Integro-Differential Equation Using Touchard Polynomials
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A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

 

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Publication Date
Wed Mar 10 2021
Journal Name
Baghdad Science Journal
Approximated Methods for Linear Delay Differential Equations Using Weighted Residual Methods
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The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

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Publication Date
Fri Feb 01 2019
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of estimations methods of the entropy function to the random coefficients for two models: the general regression and swamy of the panel data
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In this study, we focused on the random coefficient estimation of the general regression and Swamy models of panel data. By using this type of data, the data give a better chance of obtaining a better method and better indicators. Entropy's methods have been used to estimate random coefficients for the general regression and Swamy of the panel data which were presented in two ways: the first represents the maximum dual Entropy and the second is general maximum Entropy in which a comparison between them have been done by using simulation to choose the optimal methods.

The results have been compared by using mean squares error and mean absolute percentage error to different cases in term of correlation valu

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Publication Date
Mon Jan 01 2007
Journal Name
Iraqi Journal Of Science
Adaptive methods for matching problem
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In this paper, we deal with the problem of general matching of two images one of them has experienced geometrical transformations, to find the correspondence between two images. We develop the invariant moments for traditional techniques (moments of inertia) with new approach to enhance the performance for these methods. We test various projections directional moments, to extract the difference between Block Distance Moment (BDM) and evaluate their reliability. Three adaptive strategies are shown for projections directional moments, that are raster (vertical and horizontal) projection, Fan-Bean projection and new projection procedure that is the square projection method. Our paper started with the description of a new algorithm that is low

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Publication Date
Sat Apr 20 2024
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
An Approximate Solution for a Second Order Elliptic Inverse Coefficient Problem with Nonlocal Integral
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This article studies the nonlocal inverse boundary value problem for a rectangular domain, a second-order, elliptic equation and a two-dimensional equation. The main objective of the article is to find the unidentified coefficient and provide a solution to the problem. The two-dimensional second-order, convection equation is solved directly using the finite difference method (FDM). However, the inverse problem was successfully solved the MATLAB subroutine lsqnonlin from the optimization toolbox after reformulating it as a nonlinear regularized least-square optimization problem with a simple bound on the unknown quantity. Considering that the problem under study is often ill-posed and that even a small error in the input data can hav

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