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.

We demonstrate the results of a mathematical model for investigation the nonlinear Stimulated Brillouin Scattering (SBS), which can be employed to achieve high optical amplifier. The SBS is created by interaction between the incident We demonstrate the results of a mathematical model for investigation the nonlinear Stimulated Brillouin Scattering (SBS), which can be employed to achieve high optical amplifier. The SBS is created by interaction between the incident light and the acoustic vibration fiber. The design criteria and the amplification characteristic of the Brillouin amplifier is demonstrated and discussed for fiber Brillouin amplifier using different pump power with different fiber length. The results show, high Brillouin gain can

In this article, a numerical method integrated with statistical data simulation technique is introduced to solve a nonlinear system of ordinary differential equations with multiple random variable coefficients. The utilization of Monte Carlo simulation with central divided difference formula of finite difference (FD) method is repeated n times to simulate values of the variable coefficients as random sampling instead being limited as real values with respect to time. The mean of the n final solutions via this integrated technique, named in short as mean Monte Carlo finite difference (MMCFD) method, represents the final solution of the system. This method is proposed for the first time to calculate the numerical solution obtained fo

In this paper, we present new algorithm for the solution of the nonlinear high order multi-point boundary value problem with suitable multi boundary conditions. The algorithm is based on the semi-analytic technique and the solutions are calculated in the form of a rapid convergent series. It is observed that the method gives more realistic series solution that converges very rapidly in physical problems. Illustrative examples are provided to demonstrate the efficiency and simplicity of the proposed method in solving this type of multi- point boundary value problems.

This research aims to investigate and evaluate a reactive powder concrete (RPC) cast using economical materials. Its mechanical properties were investigated and evaluated by studying the effects of using different cement and silica fume contents and locally steel fibers aspect ratios as reinforcement for this concrete. A compressive strength of about 155.2MPa, indirect tensile strength of 16.0MPa, modulus of elasticity of 48.7GPa, flexural strength of 43.5MPa, impact energy of 3294.4kN.m and abrasion loss 0.59%  have been achieved for reinforced RPC contains  910 kg/m³ cement content, silica fume content 185 kg/m³ of cement weight and fiber volume fraction 2%. The water absorption values w

The aim of this study was to Identifying The Effect of using Linear programming and Branching programming by computer in Learning and Retention of movement concatenation(Linkwork) in parallel bars in Artistic Gymnastics. The searchers have used the experimental method. The search subject of this article has been taken (30) male - students in the second class from the College of Physical Education/University of Baghdad divided into three groups; the first group applied linear programming by computer, and the second group has been applicated branching programming by computer, while precision group used traditional method in the college. The researchers concluded the results by using the statistical bag for social sciences (spss) such as both

The present research  investigates joints welding of 304L austenitic stainless steel using metal inert gas (MIG) welding method. The research explores the effect of process parameters (arc voltage, wire feed rate, and electrode wire diameter) on the mechanical properties of stainless steel.  The above variables are varied  respectively with 18.5, 19, 19.5 V, 116, 127, 137 mm/s, and 0.8, 1, 1.2 mm, with E308L as a filler electrode. The design matrix of the experiments was determined using the design of experiment (DOE) program Minitab 17 based on the levels of input elements used. The Taguchi orthogonal matrix methodology (Taguchi) technique was used to develop some empirical analysis for the maximum tensile strength and proper surface