The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

In The Name of Allah Most Gracious Most Merciful

The reason for choosing this topic was:

First: It is my great love for the Prophet Muhammad, may God’s prayers and peace be upon him, his family, his companions, his followers, the followers of their followers, and the scholars after them until the Day of Judgment.

Secondly: Showing a great jurisprudential figure who has contributed by speaking about important jurisprudential issues in the life of this nation, and bringing out this immortal book to put it in the hands of scholars, so I chose a figure from the followers (may God be pleased with them all).

Third: The study of the jurisprudence of the companions

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

There are many opinions about modern political thoughts for future , trying to draw a map of strong powers in the world and one of these thoughts is the conflict with civilizations. Both of these phenomena search for future and western civilization. It is important to mention that Islamic civilization has special place and clear effect through its conditions.

Throughout what mentioned above, It is obvious that the aware narrator in these biography models was the strongest tool in presenting the content, especially the biographies under study were written by feminine hands, striving to prove her identity by all means and ways. In addition, we can suppose that the hiding of she writer behind the character is no more than a mask, by which she want to mask herself so that she can express herself frankly and freely, especially when she talks about subjects that are inconsistent with the society, customs and traditions. It is important to refer that the existence of the participant narrator in the biographies under study does not prevent the presence of another narrator such as external or aware na

مستقبل الايديولوجيا واليوتوبيا في الفكر السياسي الغربي الحديث

عرض كتاب على خط النار مذكرات الرئيس الباكستاني

الوطنية والقومية والاممية والموقف الغربي والتغيير السياسي