قراءات متواترہ وشاذہ سے تفسیر قرآن

Among different ways of exegeting based on narrative method (Tafseer bil-Ma’thoor), the most reliable form is to interpret the Quran by Quran itself. There are numerous ways in which Quran elaborates its meaning one of which is the use of Qira’aat (i.e. Dialectical method). The use of different variations of reciting Quranic words elaborates its meaning. An important point to note here is that the difference in Qira’aat corroborates the diversity in the meaning and their comprehensiveness not their inconformity. Qira’aat are categorized by the scholars in two categories: There are those that are narrated and transmitted by multiplicity (Tawaatur) while others do not fulfill such criteria and are therefore denoted by the term (Shaazzah). This papers seeks to substantiate the method of interpreting the Quran by both forms of Qiraa’aat and concludes that both of these were actually revealed by Allah and are both reliable in terms of exegeting the Quranic text

Analytical Solutions to Some Nonlinear Boundary Value Problems Arising in Applied Mathematics

In this thesis, we use the Optimal Homotopy Asymptotic Method (OHAM), Differential Tranform Method (DTM), Multistage Optimal Homotopy Asymptotic Method (MOHAM), Adomian decomposition method (ADM) and Homotopy analysis method (HAM) for the solution of nonlinear initial and boundary value problems for ordinary and partial differential equations. The obtained results are compared with the results obtained from these methods and numerical results. These method do not required the linearization and discritization techniques like numerical methods andestablished better accuracy at low order approximation and its accuracy increases with increase in approximation orders; it uses a flexible auxiliary function that control the convergence of the solution and convergence region can easily be adjusted. Moreover, the procedure of these method are simple, well defined, and can easily be used the recursive relations explicitly. Except from the application of these methods, we have formulated some fluid problems and its solutions have been done. The physical interpretations of the parameters are discussed in detail. The conclusion of each model is given at the end of each chapter. The convergence regions for each problem have been mentioned graphically and the convergence is discussed. Also we have developed a new scheme for namely MOHAM which gives better accuracy not even for small domain problems but works very well for large domain boundary value problems. The implementation of this scheme is almost simple as the optimal homotopy asymptotic method.To shows its effectiveness we have used it to different bench mark problems from literature and compare the results with those obtained by other method. Fordeterminationofoptimalvaluesofconstantswe usemethodofleastsquareand collocation method for OHAM and MOHAM. For HAM h curves determine the convergence region and rate of convergence. We use Mathematica 9 for symbolic computation. Most of theworkpresentedinchapters2, 3,4,and5ofthisthesishasbeen publishedin different well reputed international journals and the remaining are submitted for possible publications. The details of published/accepted/submitted are included in the list of publications.