Preferred Language
Articles
/
3Bb8zIcBVTCNdQwCJGHd
Two efficient methods for solving Schlömilch’s integral equation
...Show More Authors
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.

Crossref
View Publication
Publication Date
Sat Jul 01 2017
Journal Name
Journal Of King Saud University - Science
A semi-analytical iterative technique for solving chemistry problems
...Show More Authors

View Publication
Crossref (19)
Crossref
Publication Date
Fri Nov 01 2013
Journal Name
Al-nahrain Journal Of Science
Modified third order iterative method for solving nonlinear equations
...Show More Authors

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

Publication Date
Sat Oct 01 2016
Journal Name
International Journal Of Pure And Apllied Mathematics
A SEMI ANALYTICAL ITERATIVE TECHNIQUE FOR SOLVING DUFFING EQUATIONS
...Show More Authors

View Publication
Crossref (13)
Crossref
Publication Date
Sat May 01 2021
Journal Name
Journal Of Physics: Conference Series
Runge-kutta Numerical Method for Solving Nonlinear Influenza Model
...Show More Authors
Abstract<p>The main object of this study is to solve a system of nonlinear ordinary differential equations (ODE) of the first order governing the epidemic model using numerical methods. The application under study is a mathematical epidemic model which is the influenza model at Australia in 1919. Runge-kutta methods of order 4 and of order 45 for solving this initial value problem(IVP) problem have been used. Finally, the results obtained have been discussed tabularly and graphically.</p>
View Publication
Scopus (9)
Crossref (3)
Scopus Crossref
Publication Date
Sat Aug 21 2021
Journal Name
Electronics
An Efficient Distributed Elliptic Positioning for Underground Remote Sensing
...Show More Authors

Remote surveying of unknown bound geometries, such as the mapping of underground water supplies and tunnels, remains a challenging task. The obstacles and absorption in media make the long-distance telecommunication and localization process inefficient due to mobile sensors’ power limitations. This work develops a new short-range sequential localization approach to reduce the required amount of signal transmission power. The developed algorithm is based on a sequential localization process that can utilize a multitude of randomly distributed wireless sensors while only employing several anchors in the process. Time delay elliptic and frequency range techniques are employed in developing the proposed algebraic closed-form solution.

... Show More
View Publication
Scopus (2)
Crossref (2)
Scopus Clarivate Crossref
Publication Date
Sun Mar 01 2015
Journal Name
5th International Conference On Energy Aware Computing Systems &amp; Applications
Area efficient test circuit for library standard cell qualification
...Show More Authors

High cost of qualifying library standard cells on silicon wafer limits the number of test circuits on the test chip. This paper proposes a technique to share common load circuits among test circuits to reduce the silicon area. By enabling the load sharing, number of transistors for the common load can be reduced significantly. Results show up to 80% reduction in silicon area due to load area reduction.

View Publication
Scopus Crossref
Publication Date
Tue Nov 01 2016
Journal Name
2016 International Conference On Advances In Electrical, Electronic And Systems Engineering (icaees)
Efficient routing algorithm for VANETs based on distance factor
...Show More Authors

There has been a great deal of research into the considerable challenge of managing of traffic at road junctions; its application to vehicular ad hoc network (VANET) has proved to be of great interest in the developed world. Dynamic topology is one of the vital challenges facing VANET; as a result, routing of packets to their destination successfully and efficiently is a non-simplistic undertaking. This paper presents a MDORA, an efficient and uncomplicated algorithm enabling intelligent wireless vehicular communications. MDORA is a robust routing algorithm that facilitates reliable routing through communication between vehicles. As a position-based routing technique, the MDORA algorithm, vehicles' precise locations are used to establish th

... Show More
View Publication
Scopus (9)
Crossref (8)
Scopus Crossref
Publication Date
Mon Oct 01 2018
Journal Name
Journal Of Economics And Administrative Sciences
Comparison of the statistical methods used to Forecast the size of the Iraqi GDP for the two sectors (public and private) for the period (2025-2016)
...Show More Authors

Gross domestic product (GDP) is an important measure of the size of the economy's production. Economists use this term to determine the extent of decline and growth in the economies of countries. It is also used to determine the order of countries and compare them to each other. The research aims at describing and analyzing the GDP during the period from 1980 to 2015 and for the public and private sectors and then forecasting GDP in subsequent years until 2025. To achieve this goal, two methods were used: linear and nonlinear regression. The second method in the time series analysis of the Box-Jenkins models and the using of statistical package (Minitab17), (GRETLW32)) to extract the results, and then comparing the two methods, T

... Show More
View Publication Preview PDF
Crossref
Publication Date
Fri Apr 26 2024
Journal Name
Mathematical Modelling Of Engineering Problems
Solving Tri-criteria: Total Completion Time, Total Earliness, and Maximum Tardiness Using Exact and Heuristic Methods on Single-Machine Scheduling Problems
...Show More Authors

View Publication
Scopus (2)
Crossref (1)
Scopus Crossref
Publication Date
Mon Sep 04 2023
Journal Name
2023 International Conference On Advanced Mechatronic Systems (icamechs)
Performance Analysis of Finite-Time Generalized Proportional Integral Observer for Uncertain Brunovsky Systems
...Show More Authors

This paper proposes a novel finite-time generalized proportional integral observer (FTGPIO) based a sliding mode control (SMC) scheme for the tracking control problem of high order uncertain systems subject to fast time-varying disturbances. For this purpose, the construction of the controller consists of two consecutive steps. First, the novel FTGPIO is designed to observe unmeasurable plant dynamics states and disturbance with its higher time derivatives in finite time rather than infinite time as in the standard GPIO. In the FTGPO estimator, the finite time convergence rate of estimations is well achieved, whereas the convergence rate of estimations by classical GPIO is asymptotic and slow. Secondly, on the basis of the finite and fast e

... Show More
View Publication
Scopus (10)
Crossref (7)
Scopus Crossref