For many problems in Physics and Computational Fluid Dynamics (CFD), providing an accurate approximation of derivatives is a challenging task. This paper presents a class of high order numerical schemes for approximating the first derivative. These approximations are derived based on solving a special system of equations with some unknown coefficients. The construction method provides numerous types of schemes with different orders of accuracy. The accuracy of each scheme is analyzed by using Fourier analysis, which illustrates the dispersion and dissipation of the scheme. The polynomial technique is used to verify the order of accuracy of the proposed schemes by obtaining the error terms. Dispersion and dissipation errors are calculated

The aim of this paper is to present method for solving ordinary differential equations of eighth order with two point boundary conditions. We propose two-point osculatory interpolation to construct polynomial solution.

The purpose of this paper is to study the instability of the zero solution of some type of nonlinear delay differential equations of fourth order by using the Lyapunov-Krasovskii functional approach; we obtain some conditions of instability of solution of such equation.

   The research tackled to solve Sudoku grid problem 9 ×9 , one of artificial intelligence problems. This problem has many of solutions in search space to generate Sudoku grid by using magic square of odd order as 3. This research concludes solution by proposed heuristic algorithm from magic square of odd order as 3 and no given numbers (from 1 to 9) in each cell of nine Sudoku grid cells in starting of problem solution, this is not similar the solution in old classic methods to generate all sub grids in Sudoku grid. The experimental results in this paper show the easily implementation to solve the problem to manage without manual method, additional to position of numbers (1, 2,..9) in center of each sub grid in Sudoku grid

The main aim of this paper is to apply a new technique suggested by Temimi and Ansari namely (TAM) for solving higher order Integro-Differential Equations. These equations are commonly hard to handle analytically so it is request numerical methods to get an efficient approximate solution. Series solutions of the problem under consideration are presented by means of the Iterative Method (IM). The numerical results show that the method is effective, accurate and easy to implement rapidly convergent series to the exact solution with minimum amount of computation. The MATLAB is used as a software for the calculations.           

The aim of this work presents the analytical studies of both the magnetohydrodynamic (MHD) flux and flow of the non-magnetohydro dynamic (MHD) for a fluid of generalized Burgers’ (GB) withinan annular pipe submitted under Sinusoidal  Pressure (SP)gradient. Closed beginning velocity's' solutions are taken by performing the finite Hankel transform (FHT) and Laplace transform (LT) of the successivefraction derivatives. Lastly, the figures were planned to exhibition the transformations effects of different fractional parameters (DFP) on the profile of velocity of both flows.

Research Summary :

         Praise be to God, Lord of the Worlds, and prayers and peace be upon the Master of the Messengers, his family and all his companions, then after:

     This is brief research that contained between its two covers one of the jurisprudence rules derived from Islamic Sharia that guarantees the right of others, in case of forcing to do the prohibited act, and it is a restriction of the rule: “Necessities allow prohibitions” and “Hardship brings facilitation” and support for the rule: “Necessities are valued.” It is an origin in alleviating the taxpayer definitely , and the study has briefly shown some of the jurisprudential appli