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.

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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

Acquires this research importance of addressing the subject (environmental problems) with
age group task, a category that children pre-school, and also reflected the importance of
research, because the (environmental problems) constitute a major threat to the continuation
of human life, particularly the children, so the environment is Bmchkladtha within
kindergarten programs represent the basis of a hub of learning where the axis, where the
kindergarten took into account included in the programs in order to help the development of
environmental awareness among children and get them used to the sound practices and
behaviors since childhood .
The research also detected problem-solving skills creative with kids Riyad

In this paper, experimental study has been done for temperature distribution in space conditioned with Ventilation Hollow Core Slab (TermoDeck) system. The experiments were carried out on a model room with dimensions of (1m 1.2m 1m) that was built according to a suitable scale factor of (1/4). The temperature distributions was measured by 59 thermocouples fixed in several locations in the test room. Two cases were considered in this work,  the first one during unoccupied period at night time (without external load) and the other at day period with external load of 800W/m² according to solar heat gain calculations during summer season in Iraq. All results confirm the use of TermoDeck system for ventilation and cooling/heat

Surfaces quality is one of the most specified customer requirements for machine parts. The major indication of surfaces quality on machined parts is surface roughness. The research aim is to study the cutting conditions and their effects on the surface roughness. This paper utilizes regression models to predict surface roughness over the machining time for variety of cutting conditions in turning. In the experimental part for turning, different types of materials (Aluminum alloy, Copper alloy, and Gray cast iron) were considered with different cutting speed ( ) and feed rate ( ). A mathematical Model depending on statistical-mathematical method between surface roughness (Rz ) and cutting condition ( , ) were derived, for the three materials