This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

The -multiple mixing ratios of γ-transitions from levels of populated in the are calculated in the present work by using the a2-ratio methods. We used the experimental coefficient (a2) for two γ-transitions from the same initial state, the statistical tensor, which is related to the a2-coefficient would be the same for the two transitions. This method was used in a previous work for pure transitions or which can be considered pure. In these cases the multiple mixing ratios for the second transition ( ) equal zero, but in our work we applied this method for mixed γ-transitions and then the multiple mixing ratio ( ) is known for one transition. Then we calculate the ( ) value and versareversa. The weight average of the -values calcu

The external shocks are one of the phenomena that the Iraqi economy is exposed to over a period of time. It is referred to as changes and events that come from outside the economic system and extends to many economic variables. However, foreign direct investment may be severely affected due to the extreme sensitivity to changes and local and international developments. This type of trauma and its characteristics to help manage and cope with external shocks, and in order to avoid the standard problems experienced by some models of simple linear regression, multi-linear regression models were used with variables Scientific and other dummy variables .

        The study foun

The present paper focuses on the study of some characteristics of
comets ions by photometry method which represent by CCD camera
which it provide seeing these images in a graded light. From 0-255
when Zero (low a light intensity) and 255 (highlight intensity). These
differences of photonic intensity can be giving us a curve which
appear from any line of this image.
From these equations the focus is concentrating on determine the
temperature distribution, velocity distribution, and intensity number
distribution which is give number of particles per unit volume.
The results explained the interaction near the cometary nucleus
which is mainly affected by the new ions added to the density of the
solar wind, th

To obtain the approximate solution to Riccati matrix differential equations, a new variational iteration approach was ‎proposed, which is suggested to improve the accuracy and increase the convergence rate of the approximate solutons to the ‎exact solution. This technique was found to give very accurate results in a few number of iterations. In this paper, the ‎modified approaches were derived to give modified solutions of proposed and used and the convergence analysis to the exact ‎solution of the derived sequence of approximate solutions is also stated and proved. Two examples were also solved, which ‎shows the reliability and applicability of the proposed approach. ‎

This paper presents new modification of HPM to solve system of 3 rd order PDEs with initial condition, for finding suitable accurate solutions in a wider domain.

The aim of this paper is to present the numerical method for solving linear system of Fredholm integral equations, based on the Haar wavelet approach. Many test problems, for which the exact solution is known, are considered. Compare the results of suggested method with the results of another method (Trapezoidal method). Algorithm and program is written by Matlab vergion 7.