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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 Mar 01 2008
Journal Name
The Third International Conference On Mathematical Sciences
On Solvability of an Operator Equation
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Publication Date
Wed Apr 28 2021
Journal Name
2021 1st Babylon International Conference On Information Technology And Science (bicits)
An Efficient Method for Stamps Verification Using Haar Wavelet Sub-bands with Histogram and Moment
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Sun Jun 05 2022
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A Computationally Efficient Gradient Algorithm for Downlink Training Sequence Optimization in FDD Massive MIMO Systems
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Future wireless networks will require advance physical-layer techniques to meet the requirements of Internet of Everything (IoE) applications and massive communication systems. To this end, a massive MIMO (m-MIMO) system is to date considered one of the key technologies for future wireless networks. This is due to the capability of m-MIMO to bring a significant improvement in the spectral efficiency and energy efficiency. However, designing an efficient downlink (DL) training sequence for fast channel state information (CSI) estimation, i.e., with limited coherence time, in a frequency division duplex (FDD) m-MIMO system when users exhibit different correlation patterns, i.e., span distinct channel covariance matrices, is to date ve

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Publication Date
Thu Jun 01 2023
Journal Name
Chemical Physics Impact
An efficient Ag decorated CeO2 synergetic catalyst for improved catalytic reduction of lethal 4-nitrophenol
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Catalytic reduction is considered an effective approach for the reduction of toxic organic pollutants from the environment, but finding an active catalyst is still a big challenge. Herein, Ag decorated CeO2 catalyst was synthesized through polyol reduction method and applied for catalytic reduction (conversion) of 4-nitrophenol (4-NP) to 4-aminophenol (4-AP). The Ag decorated CeO2 catalyst displayed an outstanding reduction activity with 99% conversion of 4-NP in 5 min with a 0.61 min−1 reaction rate (k). A number of structural characterization techniques were executed to investigate the influence of Ag on CeO2 and its effect on the catalytic conversion of 4-NP. The outstanding catalytic performances of the Ag-CeO2 catalyst can be assigne

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Publication Date
Sat Aug 25 2012
Journal Name
Wireless Personal Communications
Multi-Objective Evolutionary Algorithm Based on Decomposition for Energy Efficient Coverage in Wireless Sensor Networks
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Publication Date
Wed Jul 12 2017
Journal Name
Der Chemica Sinica
An Efficient One-Pot Approach for the Formation of Phenanthridine Derivative; Synthesis and Spectral Characterisation
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The preparation of the phenanthridine derivative compound was achieved by adopting an efficient one-pot synthetic approach. The condensation of an ethanolic mixture of benzaldehyde, cyclohexanone and ammonium acetate in a 2:1:1 mole ratio resulted in the formation of the title compound. Analytical and spectroscopic techniques were used to confirm the nature of the new compound. A mechanism for the formation of the phenanthridine moiety that is based on three steps has been suggested

Publication Date
Sun Sep 06 2015
Journal Name
Baghdad Science Journal
A New Three Step Iterative Method without Second Derivative for Solving Nonlinear Equations
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In this paper , an efficient new procedure is proposed to modify third –order iterative method obtained by Rostom and Fuad [Saeed. R. K. and Khthr. F.W. New third –order iterative method for solving nonlinear equations. J. Appl. Sci .7(2011): 916-921] , using three steps based on Newton equation , finite difference method and linear interpolation. Analysis of convergence is given to show the efficiency and the performance of the new method for solving nonlinear equations. The efficiency of the new method is demonstrated by numerical examples.

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Crossref
Publication Date
Sat Oct 28 2023
Journal Name
Baghdad Science Journal
Newton-Kantorovich Method for Solving One of the Non-Linear Sturm-Liouville Problems
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Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

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Mon Aug 01 2022
Journal Name
Baghdad Science Journal
Accurate Four-Step Hybrid Block Method for Solving Higher-Order Initial Value Problems
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This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

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Publication Date
Fri May 01 2020
Journal Name
Journal Of Physics: Conference Series
Recent modification of Homotopy perturbation method for solving system of third order PDEs
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This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

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