The aim of this paper is to propose a reliable iterative method for resolving many types of Volterra - Fredholm Integro - Differential Equations of the second kind with initial conditions. The series solutions of the problems under consideration are obtained by means of the iterative method. Four various problems are resolved with high accuracy to make evident the enforcement of the iterative method on such type of integro differential equations. Results were compared with the exact solution which exhibits that this technique was compatible with the right solutions, simple, effective and easy for solving such problems. To evaluate the results in an iterative process the MATLAB is used as a math program for the calculations.

In this paper Volterra Runge-Kutta methods which include: method of order two and four will be applied to general nonlinear Volterra integral equations of the second kind. Moreover we study the convergent of the algorithms of Volterra Runge-Kutta methods. Finally, programs for each method are written in MATLAB language and a comparison between the two types has been made depending on the least square errors.

in this paper the collocation method will be solve ordinary differential equations of retarted arguments also some examples are presented in order to illustrate this approach

Scheduling Timetables for courses in the big departments in the universities is a very hard problem and is often be solved by many previous works although results are partially optimal. This work implements the principle of an evolutionary algorithm by using genetic theories to solve the timetabling problem to get a random and full optimal timetable with the ability to generate a multi-solution timetable for each stage in the collage. The major idea is to generate course timetables automatically while discovering the area of constraints to get an optimal and flexible schedule with no redundancy through the change of a viable course timetable. The main contribution in this work is indicated by increasing the flexibility of generating opti

This paper presents a new transform method to solve partial differential equations, for finding suitable accurate solutions in a wider domain. It can be used to solve the problems without resorting to the frequency domain. The new transform is combined with the homotopy perturbation method in order to solve three dimensional second order partial differential equations with initial condition, and the convergence of the solution to the exact form is proved. The implementation of the suggested method demonstrates the usefulness in finding exact solutions. The practical implications show the effectiveness of approach and it is easily implemented in finding exact solutions.

       Finally, all algori

Algorithms using the second order of B -splines [B (x)] and the third order of B -splines [B,3(x)] are derived to solve 1' , 2nd and 3rd linear Fredholm integro-differential equations (F1DEs). These new procedures have all the useful properties of B -spline function and can be used comparatively greater computational ease and efficiency.The results of these algorithms are compared with the cubic spline function.Two numerical examples are given for conciliated the results of this method.

In this paper, a method based on modified adomian decomposition method for solving Seventh order integro-differential equations (MADM). The distinctive feature of the method is that it can be used to find the analytic solution without transformation of boundary value problems. To test the efficiency of the method presented two examples are solved by proposed method.

In this work, silicon nitride (Si₃N₄) thin films were deposited on metallic substrates (aluminium and titanium sheets) by the DC reactive sputtering technique using two different silicon targets (n-type and p-type Si wafers) as well as two Ar:N₂ gas mixing ratios (50:50 and 70:30). The electrical conductivity of the metallic (aluminium and titanium) substrates was measured before and after the deposition of silicon nitride thin films on both surfaces of the substrates. The results obtained from this work showed that the deposited films, in general, reduced the electrical conductivity of the substrates, and the thin films prepared from n-type silicon targets using a 50:50 mixing ratio and deposited on both

The aim of present work is to improve mechanical and fatigue properties for Aluminum alloy7049 by using Nano composites technique. The ZrO₂ with an average grain diameter of 30-40 nm, was selected as Nano particles, to reinforce Aluminum alloy7049 with different percentage as, 2, 4, 6 and 7 %. The Stir casting method was used to fabricate the Nano composites materials due to economical route for improvement and processing of metal matrix composites. The experimental results were shown that the adding of zirconium oxide (ZrO₂) as reinforced material leads to improve mechanical properties. The best percentage of improvement of mechanical properties of 7049 AA was with 4% wt. of ZrO₂ about (7.76% ) for ultim