In the present work, we use the Adomian Decomposition method to find the approximate solution for some cases of the Newell whitehead segel nonlinear differential equation which was solved previously with exact solution by the Homotopy perturbation and the Iteration methods, then we compared the results.

          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 study, we used Bayesian method to estimate scale parameter for the normal distribution. By considering three different prior distributions such as the square root inverted gamma (SRIG) distribution and the non-informative prior distribution and the natural conjugate family of priors. The Bayesian estimation based on squared error loss function, and compared it with the classical estimation methods to estimate the scale parameter for the normal distribution, such as the maximum likelihood estimation and th

In this paper, we used maximum likelihood method and the Bayesian method to estimate the shape parameter (θ), and reliability function (R(t)) of the Kumaraswamy distribution with two parameters l , θ (under assuming the exponential distribution, Chi-squared distribution and Erlang-2 type distribution as prior distributions), in addition to that we used method of moments for estimating the parameters of the prior distributions. Bayes

Abstract:The optimum design of the magnetic deflector with the lowest values of the radial and spiral distortion aberration coefficients was computed. The optimized calculations were made using three models, Glaser bell-shaped, Grivet-lenz and exponential models. By using the optimum axial field distribution, the pole pieces shape which gave rise to those field distributions was found by using the reconstruction method. The calculations show that the results of the three models coincide at the lower values of the excitation parameter. In general the Glaser- bell shaped model gives the optimum results at the whole range of the excitation parameter under investigation.The negative values of the spiral distortion aberration coefficient appears

Abstract  

  In this work, two algorithms of Metaheuristic algorithms were hybridized. The first is Invasive Weed Optimization algorithm (IWO) it is a numerical stochastic optimization algorithm and the second is Whale Optimization Algorithm (WOA) it is an algorithm based on the intelligence of swarms and community intelligence. Invasive Weed Optimization Algorithm (IWO) is an algorithm inspired by nature and specifically from the colonizing weeds behavior of weeds, first proposed in 2006 by Mehrabian and Lucas. Due to their strength and adaptability, weeds pose a serious threat to cultivated plants, making them a threat to the cultivation process. The behavior of these weeds has been simulated and used in Invas

Interval methods for verified integration of initial value problems (IVPs) for ODEs have been used for more than 40 years. For many classes of IVPs, these methods have the ability to compute guaranteed error bounds for the flow of an ODE, where traditional methods provide only approximations to a solution. Overestimation, however, is a potential drawback of verified methods. For some problems, the computed error bounds become overly pessimistic, or integration even breaks down. The dependency problem and the wrapping effect are particular sources of overestimations in interval computations. Berz (see [1]) and his co-workers have developed Taylor model methods, which extend interval arithmetic with symbolic computations. The latter is an ef