In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

Deep drawing process to produce square cup is very complex process due to a lot of process parameters which control on this process, therefore associated with it many of defects such as earing, wrinkling and fracture. Study of the effect of some process parameters to determine the values of these parameters which give the best result, the distributions for the thickness and depths of the cup were used to estimate the effect of the parameters on the cup numerically, in addition to experimental verification just to the conditions which give the best numerical predictions in order to reduce the time, efforts and costs for producing square cup with less defects experimentally is the aim of this study. The numerical analysis is used to study

This study is dedicated to solving multicollinearity problem for the general linear model by using Ridge regression method. The basic formulation of this method and suggested forms for Ridge parameter is applied to the Gross Domestic Product data in Iraq. This data has normal distribution. The best linear regression model is obtained after solving multicollinearity problem with the suggesting of 10 k value.

The aim for this research is to investigate the effect of inclusion of crack incidence into the 2D numerical model of the masonry units and bonding mortar on the behavior of unreinforced masonry walls supporting a loaded reinforced concrete slab. The finite element method was implemented for the modeling and analysis of unreinforced masonry walls. In this paper, ABAQUS, FE software with implicit solver was used to model and analyze unreinforced masonry walls which are subjected to a vertical load. Detailed Micro Modeling technique was used to model the masonry units, mortar and unit-mortar interface separately. It was found that considering potential pure tensional cracks located vertically in the middle of the mortar and units show

Due to wind wave actions, ships impacts, high-speed vehicles and others resources of loading, structures such as high buildings rise bridge and electric transmission towers undergo significant coupled moment loads. In this study, the effect of increasing the value of coupled moment and increasing the rigidity of raft footing on the horizontal deflection by using 3-D finite element using ABAQUS program. The results showed that the increasing the coupled moment value leads to an increase in lateral deflection and increase in the rotational angle (α◦). The rotational angle increases from (0.014, 0.15 to 0.19) at coupled moment (120 kN.m), (0.29, 0.31 and 0.49) at coupled moment (240 kN.m) and (0.57, 0.63 and 1.03) at cou

The wavelets have many applications in engineering and the sciences, especially mathematics. Recently, in 2021, the wavelet Boubaker (WB) polynomials were used for the first time to study their properties and applications in detail. They were also utilized for solving the Lane-Emden equation. The aim of this paper is to show the truncated Wavelet Boubaker polynomials for solving variation problems. In this research, the direct method using wavelets Boubaker was presented for solving variational problems. The method reduces the problem into a set of linear algebraic equations. The fundamental idea of this method for solving variation problems is to convert the problem of a function into one that involves a finite number of variables. Diff