We present a reliable algorithm for solving, homogeneous or inhomogeneous, nonlinear ordinary delay differential equations with initial conditions. The form of the solution is calculated as a series with easily computable components. Four examples are considered for the numerical illustrations of this method. The results reveal that the semi analytic iterative method (SAIM) is very effective, simple and very close to the exact solution demonstrate reliability and efficiency of this method for such problems.

تعلمنا في المدارس بأن ارتكاب الاخطاء شيء غير مقبول، وقد تهتز مكانتنا بسببها، وعندما نتخرج من معاهدنا وكلياتنا، ونحصل على شهاداتنا العلمية، وندخل عالم العمل يستمر كرهنا وامتعاظنا لها. وبناءاً على ذلك، نحاول بذل قصارى جهدنا لتحاشي الاخطاء مهما كانت بسيطة، وقد نقوم احياناً بإخفائها، او تحويل لوم وقوعها على الغير. ففي هذه الحالة، ندفع اثماناً باهضة لأخطانئا، وقد يصل الأمر الى خسارة وظائفنا لا بل حياتنا في

Numerical study has been conducted to investigate the thermal performance enhancement of flat plate solar water collector by integrating the solar collector with metal foam blocks.The flow is assumed to be steady, incompressible and two dimensional in an inclined channel. The channel is provided with eight foam blocks manufactured form copper. The Brinkman-Forchheimer extended Darcy model is utilized to simulate the flow in the porous medium and the Navier-Stokes equation in the fluid region. The energy equation is used with local thermal equilibrium (LTE) assumption to simulate the thermofield inside the porous medium. The current investigation covers a range of solar radiation intensity at 09:00 AM, 12:00 PM, and 04:00

This paper experimentally investigates the heating process of a hot water supply using a neural network implementation of a self-tuning PID controller on a microcontroller system. The Particle Swarm Optimization (PSO) algorithm employed in system tuning proved very effective, as it is simple and fast optimization algorithm. The PSO method for the PID parameters is executed on the Matlab platform in order to put these parameters in the real-time digital PID controller, which was experimented with in a pilot study on a microcontroller platform. Instead of the traditional phase angle power control (PAPC) method, the Cycle by Cycle Power Control (CBCPC) method is implemented because it yields better power factor and eliminates harmonics

The Aim of this paper is to investigate numerically the simulation of ice melting in one and two dimension using the cell-centered finite volume method. The mathematical model is based on the heat conduction equation associated with a fixed grid, latent heat source approach. The fully implicit time scheme is selected to represent the time discretization. The ice conductivity is chosen
to be the value of the approximated conductivity at the interface between adjacent ice and water control volumes. The predicted temperature distribution, percentage melt fraction, interface location and its velocity is compared with those obtained from the exact analytical solution. A good agreement is obtained when comparing the numerical results of one

Scholars have inherited a tremendous wealth in all sciences and knowledge, especially jurisprudence; therefore, the students of forensic science had to execute this precious heritage, achieving a serious scientific investigation; So I opted for the realization of this part of the Book of Leasing for the small book of fatwas of Yusuf bin Ahmed al-Khasi.

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

<p>Daftardar Gejji and Hossein Jafari have proposed a new iterative method for solving many of the linear and nonlinear equations namely (DJM). This method proved already the effectiveness in solved many of the ordinary differential equations, partial differential equations and integral equations. The main aim from this paper is to propose the Daftardar-Jafari method (DJM) to solve the Duffing equations and to find the exact solution and numerical solutions. The proposed (DJM) is very effective and reliable, and the solution is obtained in the series form with easily computed components. The software used for the calculations in this study was MATHEMATICA^® 9.0.</p>

The aim of this paper is to derive a posteriori error estimates for semilinear parabolic interface problems. More specifically, optimal order a posteriori error analysis in the - norm for semidiscrete semilinear parabolic interface problems is derived by using elliptic reconstruction technique introduced by Makridakis and Nochetto in (2003). A key idea for this technique is the use of error estimators derived for elliptic interface problems to obtain parabolic estimators that are of optimal order in space and time.

 According to the circumstances experienced by our country which led to Occurrence of many crises that are the most important crisis is gaining fuel therefore , the theory of queue ( waiting line ) had been used to solve this crisis and as the relevance of this issue indirect and essential role in daily life  .

This research aims to conduct a study of the distribution of gasoline station in (both sides AL – kharkh and AL Rusafa, for the purpose of reducing wasting time and services time through the criteria of the theory of queues and work to improve the efficiency of these stations by the other hand. we are working to reduce the cost of station and increase profits by reducing the active serv