آتم کتھا
وہ مجھ سے اس وقت بچھڑا تھا
جب آنکھوں کے سیپ خوابوں کے موتیوں کوترستے تھے
جب جسم و جاںپر رنگِ بہار نہیں چڑھا تھا
جب روح احساسِ کرب سے نا آشنا تھی
زندگی کی حقیقت کا ادراک نہیں تھا
کوئی دوست تھا نہ دشمن
اب میرے پاس سب کچھ ہے
یادیں ،محرومیاں ،اذیتیں
کیسے انمول کھلونے ہیں
مگر افسوس بے فکری کی دولت چھن گئی
Financial dealings are an integral part of human life. All the human beings have to do such dealings for their needs, mostly related to trade. But principles and rules for such dealings depend on either human intellect or the Shariah teachings. The human intellect in itself prevents humans from indulging into oppressive and corrupt ways of earning so that they do not incur loss in trading. But selfish and lustrous worldly interests mislead them, and consequently, they take to the prohibited ways of earning. In such situations, Shariah guides us to the right path. Allah Ta’ala has guided the mankind in the best way through the eternal and everlasting teachings of the Holy Quran. Regarding the financial dealings, this Holy Book has given us a comprehensive guideline which is beyond human intellect, and that is: Do not get one another’s possessions through prohibited ways; yes, you can earn them through trading based on mutual consent. This guideline has prohibited all the illegal ways of earning, including fraudulence, dishonesty, misrepresentation etc. The Article in focus discusses the condemnation of earning through prohibited ways, importance of the unambiguity of financial dealings and the related Shariah rulings.
Nonlinear partial differential equations are often used to understand and model nonlinear processes arising in many branches of science and engineering. For most of partial differential equations a general closed-form analytical solution is not available and therefore use of numerical methods always remains an important alternative for the solution of partial differential equations. Several numerical methods are developed for the solution of partial differential equations including finite difference methods, finite element methods, spectral methods and spline methods. However numerical methods posses some limitations such as mesh generation, slow rate of convergence, spatial dependence, stability, low accuracy and difficult to implement in complex geometries. One of domain type methods is known as radial basis functions method, which is a truly meshless method, infinitely differentiable, numerically accurate, stable, very high rate of convergence, spatial independence and flexible with respect to complex geometry. The main difference between the mesh free radial basis functions method and classical mesh-based methods is that the radial basis functions can be extended to the entire domain of influence without diving into elements. In this thesis, we present mesh free radial basis functions method based on collocation principle for numerical solution of various time dependent nonlinear partial differential equations namely, Regularized Long Wave (RLW) equation, Modified Regularized Long Wave (MRLW) equation, Modified Equal Width Wave (MEW) equation, Klein- Gordon Schrödinger (KGS) equations, Klein-Gordon Zakharov (KGZ) equations, Two dimensional Coupled Burgers’ equations and Two dimensional Reaction-Diffusion Brusselator equations. Different radial basis functions are used for this purpose. First order forward and second order central difference approximation is employed to the time derivative. The elementary stability and convergence of the proposed method are discussed. Accuracy of the method is assessed in terms of various error norms, number of nodal points and time step size. Performance of the proposed method is validated through examples from literature. Apart from ease of implementation, better accuracy is obtained. Comparison with existing methods such as finite difference methods, finite element methods, boundary element methods and spline methods is made to show the superiority and simple applicability of the mesh free method.