This paper presents seven modified Adomian Decomposition Method (ADM) techniques for efficiently solving initial value problems, especially those involving non-homogeneous and nonlinear differential equations. While the classical ADM is effective for linear homogeneous cases, it has difficulties solving more complex problems. The proposed modifications—from MADM1 to MLADM—include Maclaurin and Taylor expansions, Laplace transforms, and single-step iterations.• These modifications enhance convergence, reduce complexity, and improve accuracy.• Each method offers specific advantages, such as accelerating convergence (MADM2, RADM4), simplifying computation (TSADM5), and achieving higher accuracy (MLADM).• Numerical examples confirm the accuracy and efficiency of all methods, highlighting their superiority over the classical ADM.
This paper considers a new Double Integral transform called Double Sumudu-Elzaki transform DSET. The combining of the DSET with a semi-analytical method, namely the variational iteration method DSETVIM, to arrive numerical solution of nonlinear PDEs of Fractional Order derivatives. The proposed dual method property decreases the number of calculations required, so combining these two methods leads to calculating the solution's speed. The suggested technique is tested on four problems. The results demonstrated that solving these types of equations using the DSETVIM was more advantageous and efficient
In this paper, simulation studies and applications of the New Weibull-Inverse Lomax (NWIL) distribution were presented. In the simulation studies, different sample sizes ranging from 30, 50, 100, 200, 300, to 500 were considered. Also, 1,000 replications were considered for the experiment. NWIL is a fat tail distribution. Higher moments are not easily derived except with some approximations. However, the estimates have higher precisions with low variances. Finally, the usefulness of the NWIL distribution was illustrated by fitting two data sets
In this article, we design an optimal neural network based on new LM training algorithm. The traditional algorithm of LM required high memory, storage and computational overhead because of it required the updated of Hessian approximations in each iteration. The suggested design implemented to converts the original problem into a minimization problem using feed forward type to solve non-linear 3D - PDEs. Also, optimal design is obtained by computing the parameters of learning with highly precise. Examples are provided to portray the efficiency and applicability of this technique. Comparisons with other designs are also conducted to demonstrate the accuracy of the proposed design.
In this paper, a new third kind Chebyshev wavelets operational matrix of derivative is presented, then the operational matrix of derivative is applied for solving optimal control problems using, third kind Chebyshev wavelets expansions. The proposed method consists of reducing the linear system of optimal control problem into a system of algebraic equations, by expanding the state variables, as a series in terms of third kind Chebyshev wavelets with unknown coefficients. Example to illustrate the effectiveness of the method has been presented.
Todays, World is faced an energy crisis because of a continuous increasing the consumption of fuels due to intension demand for all types of vehicles. This study is one of the efforts dealing with reduce the weight of vehicles by using a new material of sandwich steel, which consists of two skin steel sheets with core of a polymer material. Resistance spot welding (RSW) can be easily implemented on metals; however a cupper shunt tool was designed to perform the resistance welding of sandwich steel with DP800 cover sheets to resolve a non-conductivity problem of a polymer core. Numerical simulations with SORPAS®3D were employed to test the weldability of this new material and supported by many practical experiments. In conclus
... Show MoreVaginal biopsies and smears were collected from ten adult local healthy goats. Routine histological methods were carried out on vaginal biopsies and then stained with PAS stain. The smears were stained with Methylene blue. All samples were inspected under light microscope. The present study found that many constituents of the wall of the vagina, which have an important functional role, were absent; among these were the vaginal glands, goblet cells, muscularis mucosa, and lymphatic nodules. On the other hand, vagina showed special compensatory histological mechanisms, namely, the deep epithelial folds, the well-developed germinated stratum basale, the apparent basement membrane, and the profuse defensive cells, such as neutrophils, m
... Show MoreThe levels of shooting in basketball not very good appears un healthy phenomenon for age stages especially youth players on Iraq and therefore there is lower level in skills especially shooting that seems the players represent their players not good levels which cause difficult in choosing players for youth national team. The research sample were youth teams in Baghdad for season 2012-2013 their birth 1996 and the number teams (7) and after getting results and treat it statically the important ones were : there is a large number of failure attempts on success ones in basic shooting in basketball for youth teams in Baghdad teams (2012-2013) season and basic shooting have effective participation (positive relation) in youth teams ranking in B
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