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 wide time frame. Two examples are provided for showing the ability and advantages of the proposed method to approximate the solution of the power law nonlinearity of NLSEs. For pictorial representation, graphical inputs are included to represent the solution and show the precision as well as the validity of the MMRDTM.
This research explains to us the role of the Islamic religion in the issue of accuracy in speech and work, and how it is closely related to human production in his life, and Islam affirms that his idea is mainly reflected in his production, and how it affects the perception of the meaning of creativity. Therefore, our Islam affirmed the accuracy in every word or work we do to build a society in which people enjoy high quality in ethics and dedication in their work so that the Islamic system depends on humanity to preserve our rights on the other hand the research discusses the deliberate default and how it reflects on our production and how it makes it less good.
Equation Boizil used to Oatae approximate value of bladder pressure for 25 healthy people compared with Amqas the Alrotinahh ways used an indirect the catheter Bashaddam and found this method is cheap and harmless and easy
This document provides an examination of research, on combining orthogonal frequency division multiplexing (OFDM) and optical fibers in communication networks. With the increasing need for data speeds and efficient use of bandwidth experts have been exploring the connection between OFDM, valued for its ability to handle multipath interference and optimize spectral usage and optical fiber technology which provides superior data transmission capabilities with low signal loss and strong protection, against electromagnetic disturbances. The review summarizes discoveries from studies examining the pros and cons of using OFDM, in optical communication networks. It discusses obstacles like fiber nonlinearity, chromatic dispersion and the effects o
... Show MoreIn this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R3 is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.
Mathematical Subject Classificat
... Show MoreIn 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 MoreIn 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.