غربت کے خاتمہ کے لیے ازواجِ مطہرات کی مساعی

Islam as a religion is not based on empty or futile theories. Infact it intensely educates in altering a practical approach towards ones exixtence both as an individual and or a social being. It is the only religion which lead the way towards welfare/ "Falah" and Qura Calls such people Muflihon. Falah is for both render, either it is a man or a woman. Women especially Holy Prophet's wives are never leave behind in poor's uplift and public welfare. From the very beginning of UMMAHATUL-MOMINEEN (Holy Prophet's wives) are playing vital role in social or public welfare an till in this modern era and patriarchal society, they are role model to help plebians. The Islamic values as the world knows of them today were brought to light through our last messanger (P.B.U.H), assigned with the most important task in probably the most crucial era of human history. With the injustice all over the globe and the leaders of super powers in a rift with each other to dominate the world, exhausted the most important of resouces i.e. The humanity. The divine manifiesto of the Prophet Muhammad (P.B.U.H) and the lives of wives of Holy Prophet was actually based upon justice among masses and the preservation of conflict torn humanity. The intellectual wisdom of Holy Prophet's wives in the given situation was to restore order while restoring justice based upon the reformative rule of law as depicted by the Islamic ideology. The main aim of this very importatnt initiative was to reintroduce the humanity with the most important elements such as humility, mutual respect an retoration of long forgotten code of ethics. The basic foundation of our last Prophet's wives idealogy was to uplift poor whether they are Muslims or not. They successfully ordained the resurfacing, prevalence and practice of the same code of ethics. Now days many of such examples are prevalent in the world, not as a whole yet, though to a certain extent which is holding it together. The war torn and devastated west of the medieval found its solution in applying the same Islamic rule of law in their society in late 17th century and onward. It therefore can be deduced that the same code of ethics, which can be referred to the Quran, the sacred Islamic book, possibly offers the most effective solutions in order to ensure the societal and social development in current era.

Meshless Method of Lines for Numerical Solutions of Nonlinear Time Dependent Partial Differential Equations

Much of useful work being done today for numerical solution of partial differential equations involves nonlinear equations arising in different fields of science and engineering. Most widely used numerical techniques are finite differences, finite elements, spectral methods and collocation methods. However these methods face some limitations like construction of regular grid for irregular and complex geometries, slow convergence rate, stability and low accuracy. Another class of methods known as mesh free methods is expected to be superior than conventional mesh based methods in providing more accurate and stable numerical solution without any connective mesh. Meshless methods using radial basis functions are more flexible with high convergence rate. These methods provide very accurate numerical solution with low spatial resolution. The research presented in this dissertation is based on meshless method of lines using radial basis functions for numerical solutions of nonlinear time dependent partial differential equations (PDEs) namely, Generalized Kuramoto-Sivashinsky (GKS) equation, Kawahara type equations, Equal Width (EW) equation, Modified Equal Width (MEW) equation and Nonlinear Schrodinger (NLS) equation. First the spatial derivatives are discretize converting given PDE in to a system of first order ordinary differential equations (ODEs), which is then solved by classical fourth order Runge-Kutta (RK-4) scheme. Eigenvalue stability and convergence properties of the method are also discussed. Accuracy of the method is measured in terms of L2 and L¥ error norms and conservative properties of mass, momentum and energy. The present method is used to solve various numerical examples available in the literature and results are compared with existing numerical techniques. The method shows superior accuracy, ease of implementation and efficiency of meshless method.