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).
In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.
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
Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained
... Show MoreA 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.
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
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.
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
... Show MoreIn 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)
The statistical distributions study aimed to obtain on best descriptions of variable sets phenomena, which each of them got one behavior of that distributions . The estimation operations study for that distributions considered of important things which could n't canceled in variable behavior study, as result this research came as trial for reaching to best method for information distribution estimation which is generalized linear failure rate distribution, throughout studying the theoretical sides by depending on statistical posteriori methods like greatest ability, minimum squares method and Mixing method (suggested method).
The research
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