اسلامی تعلیمات کی روشنی میں خواتین کی مثبت سرگرمیاں کا تجزیاتی مطالعہ

The status, empowerment and dignity of woman in Islam is the crucial topic in the modern times. According to Islamic point of view, men and women have been created from a one soul. The main difference between them lies in the physical structure. A woman has to bring up, train and look after kids, which is the complicated task to civilize a nation. The issue of woman`s activities in Islam, is misunderstood and distorted due to misreporting of western media and misbehavior of some Muslim families. There is a large number of women scholars in Islamic history, Dr. Akram Nadwi has compiled the biographies of ten thousand female scholars in his commendable book of forty volumes. In educational system of Islam, a woman is completely free to perform educational activities for development of her nation. In social system of Islam, a woman is honored as mother, as daughter, as sister and as wife. The first converter to Islam was a woman, “Hazrat Khadijah (R.A)”. Hazrat Ayesha (R.A) was great scholar who reported many traditions from Holy Prophet( SAW). Many female Companions of Holy prophet( SAW) have performed great deeds even in the field of battlefield. There is a strong basis in Islamic history for women`s participation in positiveand constructive activities in every walk of life. Muslim women are allowed to perform research, educational, national,  religious, social, and financial and other constructive activities. In this research paper, Islamic overview has been described upon positive and constructive activities of women in the light of Islamic teachings.

Analytical Algorithms: Some Modifications and Applications

Initial and boundary value problems arise in different fields of mathematics and engineering. They are a result of mathematical modeling of various real-life phenomena. Some of these models are of higher nonlinearity. Thus, an exact solution of such a problem is very less likely. For those kinds of problems, we see different approximation methods, both analytical and numerical. The subject of this study is to work out some analytical algorithms that can be used to obtained solutions of nonlinear problems. A major issue with series solution algorithms is the convergence of these methods, especially for the cases of semi-infinite domain. We have tried to address this issue and have developed some modified algorithms that can work even where the traditional ones fail. Techniques like variational iteration method (VIM), variation of parameters method (VPM) and homotopy perturbation method (HPM) have been improved. This study is supposed to help the research community to remove some inbuilt deficiencies (such as divergent results, small parameter assumptions, need of perturbation, huge computational work and very limited convergence) of these traditional techniques. Efforts have been made to modify these analytical techniques. The modified schemes so obtained are free from these deficiencies. The modified schemes, like variation of parameters method with auxiliary parameter (VPMAP), optimal variation of parameters method with Adomian’s polynomials (OVPMAP), optimal variational iteration method (OVIM), optimal variational iteration method with Adomian’s polynomials (OVIMAP) and optimal homotopy perturbation method (OHPM) have been implemented on many problems arising in different fields of sciences such as, mathematical biology, fluid flow through different geometries, heat transfer equations related to chemical engineering etc. Convergent solutions are obtained for both bounded and unbounded domains by making an appropriate use of the developed modified versions. A brand new analytical algorithm, namely generalized iterative scheme (GIS), has also been introduced. Once can see its effectiveness for certain types of problems. Accuracy of the results is verified by comparing approximate solution with exact solutions, wherever available, or the residual error analysis.