A simple straightforward mathematical method has been developed to cluster grid nodes on a boundary segment of an arbitrary geometry that can be fitted by a relevant polynomial. The method of solution is accomplished in two steps. At the first step, the length of the boundary segment is evaluated by using the mean value theorem, then grids are clustered as desired, using relevant linear clustering functions. At the second step, as the coordinates cell nodes have been computed and the incremental distance between each two nodes has been evaluated, the original coordinate of each node is then computed utilizing the same fitted polynomial with the mean value theorem but reversibly.

The method is utilized to predict

In our article, three iterative methods are performed to solve the nonlinear differential equations that represent the straight and radial fins affected by thermal conductivity. The iterative methods are the Daftardar-Jafari method namely (DJM), Temimi-Ansari method namely (TAM) and Banach contraction method namely (BCM) to get the approximate solutions. For comparison purposes, the numerical solutions were further achieved by using the fourth Runge-Kutta (RK4) method, Euler method and previous analytical methods that available in the literature. Moreover, the convergence of the proposed methods was discussed and proved. In addition, the maximum error remainder values are also evaluated which indicates that the propo

Theoretical and experimental investigations of free convection through a cubic cavity with sinusoidal heat flux at bottom wall, the top wall is exposed to an outside ambient while the other walls are adiabatic saturated in porous medium had been approved in the present work. The range of Rayleigh number was and Darcy number values were . The theoretical part involved a numerical solution while the experimental part included a set of tests carried out to study the free convection heat transfer in a porous media (glass beads) for sinusoidal heat flux boundary condition. The investigation enclosed values of Rayleigh number (5845.6, 8801, 9456, 15034, 19188 and 22148) and angles of inclinations (0, 15, 30, 45 and 60 degree). The numerical an

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

The transportation model is a well-recognized and applied algorithm in the distribution of products of logistics operations in enterprises. Multiple forms of solution are algorithmic and technological, which are applied to determine the optimal allocation of one type of product. In this research, the general formulation of the transport model by means of linear programming, where the optimal solution is integrated for different types of related products, and through a digital, dynamic, easy illustration Develops understanding of the Computer in Excel QM program. When choosing, the implementation of the form in the organization is provided.

CO2 laser (10.6 μm) is the most often used laser in the oral surgery due to its high absorption by water of the oral tissues. Several benefits of the use of CO2 laser have been reported for oral surgical procedures. This study aims to evaluate the effect of CO2 laser on soft and hard oral tissues (in vitro study). This study was done on fresh tissues from sheep’s head. CO2Surgical Laser with different operation modes was used; 0.2 mm spot size using different laser parameters on the tongue, and bone making holes, incisions and cutting. The depths and widths of holes and incisions were measured using endodontic file under magnification. The speed of incisions was calculated and the required time for cutting was measured using sport clo