In this Paper, we proposed two new predictor corrector methods for solving Kepler's equation in hyperbolic case using quadrature formula which plays an important and significant rule in the evaluation of the integrals. The two procedures are developed that, in two or three iterations, solve the hyperbolic orbit equation in a very efficient manner, and to an accuracy that proves to be always better than 10-15. The solution is examined with and with grid size , using the first guesses hyperbolic eccentric anomaly is and , where is the eccentricity and is the hyperbolic mean anomaly.
In this paper, the methods of weighted residuals: Collocation Method (CM), Least Squares Method (LSM) and Galerkin Method (GM) are used to solve the thin film flow (TFF) equation. The weighted residual methods were implemented to get an approximate solution to the TFF equation. The accuracy of the obtained results is checked by calculating the maximum error remainder functions (MER). Moreover, the outcomes were examined in comparison with the 4th-order Runge-Kutta method (RK4) and good agreements have been achieved. All the evaluations have been successfully implemented by using the computer system Mathematica®10.
In this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
... Show MoreThe main objective of this paper is to designed algorithms and implemented in the construction of the main program designated for the determination the tenser product of representation for the special linear group.
Face recognition and identity verification are now critical components of current security and verification technology. The main objective of this review is to identify the most important deep learning techniques that have contributed to the improvement in the accuracy and reliability of facial recognition systems, as well as highlighting existing problems and potential future research areas. An extensive literature review was conducted with the assistance of leading scientific databases such as IEEE Xplore, ScienceDirect, and SpringerLink and covered studies from the period 2015 to 2024. The studies of interest were related to the application of deep neural networks, i.e., CNN, Siamese, and Transformer-based models, in face recogni
... Show MoreStenography is the art of hiding the very presence of communication by embedding secret message into innocuous looking cover document, such as digital image, videos, sound files, and other computer files that contain perceptually irrelevant or redundant information as covers or carriers to hide secret messages.
In this paper, a new Least Significant Bit (LSB) nonsequential embedding technique in wave audio files is introduced. To support the immunity of proposed hiding system, and in order to recover some weak aspect inherent with the pure implementation of stego-systems, some auxiliary processes were suggested and investigated including the use of hidden text jumping process and stream ciphering algorithm. Besides, the suggested
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