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Finding the Exact Solution of Kepler’s Equation for an Elliptical Satellite Orbit Using the First Kind Bessel Function
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     In this study, the first kind Bessel function was used to solve Kepler equation for an elliptical orbiting satellite. It is a classical method that gives a direct solution for calculation of the eccentric anomaly. It was solved for one period from (M=0-360)° with an eccentricity of (e=0-1) and the number of terms from (N=1-10). Also, the error in the representation of the first kind Bessel function was calculated. The results indicated that for eccentricity of (0.1-0.4) and (N = 1-10), the values of eccentric anomaly gave a good result as compared with the exact solution. Besides, the obtained eccentric anomaly values were unaffected by increasing the number of terms (N = 6-10) for eccentricities (0.8 and 0.9). The Bessel function's solution appeared to be close to the exact solution for eccentricity of 1 and more than 10 number of terms. Finally, the representation of the first kind Bessel function J1(x) was closer to the exact representation only for eccentricity 0.5 and (N=1-10).

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Publication Date
Sun Jun 02 2013
Journal Name
Baghdad Science Journal
Some Probability Characteristics Functions of the Solution of Stochastic Fredholm Integral Equation Contains a Known Sine Wave Function
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Abstract:In this paper, some probability characteristics functions (moments, variances,convariance, and spectral density functions) are found depending upon the smallestvariance of the solution of some stochastic Fredholm integral equation contains as aknown function, the sine wave function

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Publication Date
Sat Jul 31 2021
Journal Name
Iraqi Journal Of Science
An Approximate Solution of the Space Fractional-Order Heat Equation by the Non-Polynomial Spline Functions
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     The linear non-polynomial spline is used here to solve the fractional partial differential equation (FPDE). The fractional derivatives are described in the Caputo sense. The tensor products are given for extending the one-dimensional linear non-polynomial spline to a two-dimensional spline  to solve the heat equation. In this paper, the convergence theorem of the method used to the exact solution is proved and the numerical examples show the validity of the method. All computations are implemented by Mathcad15.

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Publication Date
Thu Dec 02 2021
Journal Name
Iraqi Journal Of Science
Approximate Solution for advection dispersion equation of time Fractional order by using the Chebyshev wavelets-Galerkin Method
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The aim of this paper is adopted to give an approximate solution for advection dispersion equation of time fractional order derivative by using the Chebyshev wavelets-Galerkin Method . The Chebyshev wavelet and Galerkin method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are described based on the Caputo sense. Illustrative examples are included to demonstrate the validity and applicability of the proposed technique.

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Publication Date
Sun Jul 29 2018
Journal Name
Iraqi Journal Of Science
A new approximate solution for the Telegraph equation of space-fractional order derivative by using Sumudu method
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In this work, we are concerned with how to find an explicit approximate solution (AS) for the telegraph equation of space-fractional order (TESFO) using Sumudu transform method (STM). In this method, the space-fractional order derivatives are defined in the Caputo idea. The Sumudu method (SM) is established to be reliable and accurate. Three examples are discussed to check the applicability and the simplicity of this method. Finally, the Numerical results are tabulated and displayed graphically whenever possible to make comparisons between the AS and exact solution (ES).

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Publication Date
Mon Mar 08 2021
Journal Name
Baghdad Science Journal
An approximate solution for solving linear system of integral equation with application on "Stiff" problems
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An approximate solution of the liner system of ntegral cquations fot both fredholm(SFIEs)and Volterra(SIES)types has been derived using taylor series expansion.The solusion is essentailly

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Publication Date
Mon Mar 09 2015
Journal Name
Monthly Notices Of The Royal Astronomical Society
A reliable iterative method for solving Volterra integro-differential equations and some applications for the Lane–Emden equations of the first kind
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Publication Date
Sun May 17 2020
Journal Name
Iraqi Journal Of Science
On Existence and Uniqueness of an Integrable Solution for a Fractional Volterra Integral Equation on 𝑹+
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In this paper, by using the Banach fixed point theorem, we prove the existence and uniqueness theorem of a fractional Volterra integral equation in the space of Lebesgue integrable 𝐿1(𝑅+) on unbounded interval [0,∞).

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Publication Date
Wed May 31 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Studying of Optical System Includes Elliptical Aperture Point Spread Function
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In this work, optical system with elliptical aperture using point spread function was studied. This is due to its comparison with an optical system with a circular aperture. The present work deals with the theoretical study of intensity distribution within the image. In this work, a special formula was derived which is called the point spread function (PSF) by using a pupil function technique. The work deals with the limited optical system diffraction only (ideal system), and the system with focal shift. Also a graphic relation was founded between eccentricity and the best of focal depth given to at least (80%) of intensity.

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Publication Date
Fri Jan 01 2016
Journal Name
Journal Of Computer And Communications
Parallel Quick Search Algorithm for the Exact String Matching Problem Using OpenMP
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String matching is seen as one of the essential problems in computer science. A variety of computer applications provide the string matching service for their end users. The remarkable boost in the number of data that is created and kept by modern computational devices influences researchers to obtain even more powerful methods for coping with this problem. In this research, the Quick Search string matching algorithm are adopted to be implemented under the multi-core environment using OpenMP directive which can be employed to reduce the overall execution time of the program. English text, Proteins and DNA data types are utilized to examine the effect of parallelization and implementation of Quick Search string matching algorithm on multi-co

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Publication Date
Mon May 15 2017
Journal Name
Ibn Al-haitham Journal For Pure And Applied Sciences
Open Newton Contes Formula for Solving Linear Voltera Integro-Differential Equation of the First Order
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  In this work, some of numerical methods for solving first order linear Volterra IntegroDifferential Equations are presented.      The numerical solution of these equations is obtained by using Open Newton Cotes formula.      The Open Newton Cotes formula is applied to find the optimum solution for this equation.      The computer program is written in (MATLAB) language (version 6)

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