Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions exhibited unstable behavior, with distinct, insignificant peaks disappearing as z increased. In comparison to other published studies in this section, the results showed good agreement.
In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth
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This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived. In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.
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In this work a study and calculation of the normal approach between two bodies,
spherical and rough flat surface, had been conducted by the aid of image processing
technique. Four kinds of metals of different work hardening index had been used as a
surface specimens and by capturing images of resolution of 0.006565 mm/pixel a good estimate of the normal approach may be obtained the compression tests had been done in strength of material laboratory in mechanical engineering department, a Monsanto tensometer had been used to conduct the indentation tests. A light section measuring equipment microscope BK 70x50 was used to calculate the surface parameters of the texture profile like standard deviation of asperity peak heights
In this work a study and calculation of the normal approach between two bodies, spherical and rough flat surface, had been conducted by the aid of image processing technique. Four kinds of metals of different work hardening index had been used as a surface specimens and by capturing images of resolution of 0.006565 mm/pixel a good estimate of the normal approach may be obtained the compression tests had been done in strength of material laboratory in mechanical engineering department, a Monsanto tensometer had been used to conduct the indentation tests.
A light section measuring equipment microscope BK 70x50 was used to calculate the surface parameters of the texture profile like standard deviation of asperity peak heights, centre lin
The UN plans to achieve several development objectives by 2030. These objectives address global warming, a major issue. This method aims to improve sustainable accounting performance (AP). In this circumstance, AI is being applied in various fields, notably in economic, social, and environmental (ESE) domains. This research investigates how sustainable development (SD) influences AI methodologies and AP improvement. The research examined a sample of Iraqi banks listed on the Iraq Stock Exchange from 2014 to 2022. AI was measured by ATM and POS prevalence. A three-dimensional approach examined economic, social, and environmental (ESE) sustainability. Meanwhile, the performance of sustainable accounting was measured through the return on asse
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To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which shows the reliability and applicability of the proposed approach.
Improving" Jackknife Instrumental Variable Estimation method" using A class of immun algorithm with practical application