This paper introduces the Multistep Modified Reduced Differential Transform Method (MMRDTM). It is applied to approximate the solution for Nonlinear Schrodinger Equations (NLSEs) of power law nonlinearity. The proposed method has some advantages. An analytical approximation can be generated in a fast converging series by applying the proposed approach. On top of that, the number of computed terms is also significantly reduced. Compared to the RDTM, the nonlinear term in this method is replaced by related Adomian polynomials prior to the implementation of a multistep approach. As a consequence, only a smaller number of NLSE computed terms are required in the attained approximation. Moreover, the approximation also converges rapidly over a

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  This study is concerned with the estimation of constant  and time-varying parameters in non-linear ordinary differential equations, which do not have analytical solutions. The estimation is done in a multi-stage method where constant and time-varying parameters are estimated in a straight sequential way from several stages. In the first stage, the model of the differential equations is converted to a regression model that includes the state variables with their derivatives and then the estimation of the state variables and their derivatives in a penalized splines method and compensating the estimations in the regression model. In the second stage, the pseudo- least squares method was used to es

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

In this work, the effect of variation of semi-angle of the conical part on the vibration characteristics of cylindrical-conical coupled structure is investigated. The shell is made of polyester resin reinforced by continuous E-glass fibers. The case is analyzed experimentally and numerically for orthotropic shell structures. The experimental program is conducted by exciting the fabricated structure by an impact hammer and monitoring the response using an attached accelerometer for different semi-angles of the conical part.
Software named SIGVIEW is used to perform the signal processing on the acquired signal in order to measure the natural frequencies and the corresponding mode shapes. The numerical investigation is achieved using ANS

AA wahid, journal mustansiriyah of sports science, 2023

In this paper, a computational method for solving optimal problem is presented, using indirect method (spectral methodtechnique) which is based on Boubaker polynomial. By this method the state and the adjoint variables are approximated by Boubaker polynomial with unknown coefficients, thus an optimal control problem is transformed to algebraic equations which can be solved easily, and then the numerical value of the performance index is obtained. Also the operational matrices of differentiation and integration have been deduced for the same polynomial to help solving the problems easier. A numerical example was given to show the applicability and efficiency of the method. Some characteristics of this polynomial which can be used for solvin

           In this paper, the homotopy perturbation method (HPM) is presented for treating a linear system of second-kind mixed Volterra-Fredholm integral equations. The method is based on constructing the series whose summation is the solution of the considered system. Convergence of constructed series is discussed and its proof is given; also, the error estimation is obtained. Algorithm is suggested and applied on several examples and the results are computed by using MATLAB (R2015a). To show the accuracy of the results and the effectiveness of the method, the approximate solutions of some examples are compared with the exact solution by computing the absolute errors.

This paper offers a systemic review of the deep learning methods to detect violence on campus, which is a critical issue in intelligent surveillance to improve the student safety and prompt cut off of violent accidents. The review reviews studies published 2018-2025, concentrating on model structure to detect fights, bullying, vandalism, and aggressive behavior on problematic campuses due to occlusion and light variations and complicated human interactions. The research design includes a comparative study of different deep learning networks, such as CNNs, RNNs, 3D CNNs, attention-based networks, transformers, graph neural networks, neuro-fuzzy, and multimodal systems and federated learning methods. The paper also assesses benchmark