This paper focuses on developing a self-starting numerical approach that can be used for direct integration of higher-order initial value problems of Ordinary Differential Equations. The method is derived from power series approximation with the resulting equations discretized at the selected grid and off-grid points. The method is applied in a block-by-block approach as a numerical integrator of higher-order initial value problems. The basic properties of the block method are investigated to authenticate its performance and then implemented with some tested experiments to validate the accuracy and convergence of the method.

Due to its importance in physics and applied mathematics, the non-linear Sturm-Liouville problems
witnessed massive attention since 1960. A powerful Mathematical technique called the Newton-Kantorovich
method is applied in this work to one of the non-linear Sturm-Liouville problems. To the best of the authors’
knowledge, this technique of Newton-Kantorovich has never been applied before to solve the non-linear
Sturm-Liouville problems under consideration. Accordingly, the purpose of this work is to show that this
important specific kind of non-linear Sturm-Liouville differential equations problems can be solved by
applying the well-known Newton-Kantorovich method. Also, to show the efficiency of appl

Biodiesel is becoming one of the most attractive alternative biofuels for petroleum-based diesel fuels. The castor plant is one of the abundant non-edible oils found in many countries. This paper aims to study Libyan castor oil and its potential for diesel conversion. Experiments were carried out in the laboratories of the Specific Center for Training in the Oil Industries in Al-Zawiya. The oil was extracted using a Soxhlet extractor and n-hexane solvent at 60 °C. Transesterification reactions were conducted in a batch reactor (a three-neck flask was used, where the middle opening carries a reflux condensation unit) at 65 °C. The methanol-to-castor oil molar ratio was 6:1, with a catalyst concentration of 1 wt.% relative to the ca

This study examined the problematic of the ambiguous relationship between the media and terrorism and the problems that result from press coverage of terroristic incidents. The paper sought to show the classification and confrontation of such incidents had been established from the point of view of a sample of media professionals, researchers and writers who are frequenters of Al-Mutanabi Street in Baghdad. The media outlets that carry this coverage would not give up their media mission as well as the terrorists would not be given an opportunity to take advantage of this coverage in achieving their goals and objectives. Furthermore, the terrorist organizations would have no chance to exploit these means to deliver their terroristic messa

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.

The study of surface hardness, wear resistance, adhesion strength, electrochemical corrosion resistance and thermal conductivity of coatings composed from sodium silicate was prepared using graphite micro-size particles and carbon nano particles as fillers respectively of concentration of (1-5%), for the purpose of covering and protecting the oil distillation towers. The results showed that the sodium silicate coating reinforced with carbon nano-powder has higher resistance to stitches, mechanical wear, adhesive and thermal conductivity than graphite/sodium silicate composite especially when the ratio 5% and 1%, the electrochemical corrosion test confirmed that the coating process of stainless steel 304 lead to increasin

In this study two types of extraction solvents were used to extract the undesirable polyaromatics, the first solvent was furfural which was used today in the Iraqi refineries and the second was NMP (N-methyl-2-pyrrolidone).
The studied effecting variables of extraction are extraction temperature ranged from 70 to 110°C and solvent to oil ratio in the range from 1:1 to 4:1.
The results of this investigation show that the viscosity index of mixed-medium lubricating oil fraction increases with increasing extraction temperature and reaches 107.82 for NMP extraction at extraction temperature 110°C and solvent to oil ratio 4:1, while the viscosity index reaches to 101 for furfural extraction at the same extraction temperature and same

Abstract

The use of modern scientific methods and techniques, is considered important topics to solve many of the problems which face some sector, including industrial, service and health. The researcher always intends to use modern methods characterized by accuracy, clarity and speed to reach the optimal solution and be easy at the same time in terms of understanding and application.

the research presented this comparison between the two methods of solution for linear fractional programming models which are linear transformation for Charnas & Cooper , and denominator function restriction method through applied on the oil heaters and gas cookers plant , where the show after reac