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حکیم شریف الدین بقائی

حکیم شریف الدین بقائی
دہلی کی ایک عظیم خاندانی شخصیت اوربزرگان دین کے محب ِ خاص حکیم شریف الدین بقائی ۲؍ جنوری ۱۹۹۰ء کواس جہانِ فانی سے کوچ کرگئے۔اِنَّالِلّٰہِ وَاِنَّا اِلَیْہِ راجعُون۔
مرحوم بقائی انتہائی نیک،عابد وزاہد اور مُخیر تھے۔دینی اداروں سے ان کی وابستگی قابل قدر تھی۔ادارہ ندوۃ المصنفین کے قدیم ترین ممبر تھے اور حضرت مفتی عتیق الرحمن عثمانی صاحب ؒسے ان کا بڑاہی قریبی تعلق وشغف تھا۔بلکہ یہ کہنا زیادہ مناسب ہوگاکہ حکیم شریف الدین بقائی مفتی صاحبؒ کے شیدائی تھے۔مفتی صاحب کے ساتھ اکثر ان کی نشست رہتی تھی۔ان کے انتقال سے جہاں ان کے متعلقین اوردلّی والوں کوصدمہ عظیم ہواہے،وہیں ادارہ ندوۃ المصنفین وبرہان بھی اپنے قدیم ترین مخلص سے محروم ہوجانے کی وجہ سے سخت رنج وغم سے دوچار ہے۔ ان کے لائق ہونہار صاحبزادے ڈاکٹر معین الدین بقائی سے اظہار تعزیت کرتے ہوئے ادارہ مرحوم کی مغفرت کے لیے دعاگو ہے۔ [جنوری ۱۹۹۰ء]

 

An Analytical Study of the Outcomes and Impacts of Religious Education of Pakistan, the Challenges and Opportunities

This study focuses on the impact of Religious Education in Pakistan at individual and collective levels. The research discusses the educational basis for the study of religion and analyzes the contribution of religious education towards the intellectual growth of individuals. The study raises few questions regarding religious education in Pakistan such as; why has our education system been divided into religious and secular education system. Whether the existing religious education is able to create a linkage between religion and society or not, if not what are the areas which need to be focused. What are the possibilities of sidelining the religious education and what could be its effects. The research focuses on the aims and objectives or religious education in Pakistan by analyzing the nature of curriculums of religious education at various levels. This study highlights the deficiency of the inclusion of the teachings of other religions in our religious education. The research consists of a current survey of the said topic, some findings and conclusions on the issue and few recommendations as well.

Analysis and Applications of the Optimal Homotopy Asymptotic Method to Nonlinear Initial and Boundary Value Problems

In this thesis, we use the standard optimal homotopy asymptotic method 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 by application of Adomian Decomposition Method, Variational Iteration Method, Homotopy Analysis Method, Homotopy Perturbation Method, Numerical Methods, Differential Transform Method, Double Optimal Linearization Method etc. The optimal homotopy asymptotic method does not required the assumption of initial guess and linearization like Adomian Decomposition Method, Variational Iteration Method, Homotopy Analysis Method, Homotopy Perturbation Method. The optimal homotopy asymptotic method established 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 this method is simple, well defined, and can easily be used the recursive relations explicitly. The numerical results obtained by optimal homotopy asymptotic method revealed high accuracy and excellent agreement with the exact solutions. Except from the application of optimal homotopy asymptotic method, we have extended the formulation of optimal homotopy asymptotic method to a generalized system of ordinary and partial differential equations. These extended formulations have been implemented for a system of two, three and five equations. The results obtained from extended formulations are compared with the results of known methods like Adomian Decomposition Method, Variational Iteration Method, Homotopy Analysis Method, Homotopy Perturbation Method etc, which provides that the extended formulation gives good results than other methods. Like the optimal homotopy asymptotic method the extended formulation of optimal homotopy asymptotic method provides better accuracy at low order approximation and the accuracy increases with the increase of approximation orders. Also we have developed a new scheme for differential-difference equations in the optimal homotopy asymptotic method. 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. This new scheme is extended for coupled differentialdifference equations and implemented which provides better results than Adomian Decomposition Method, Variational Iteration Method, Homotopy Analysis Method, Homotopy Perturbation Method etc and excellent agreement with the exact solutions. We used well known methods, Method of least square, Galerkin’s Method and Collocation method for finding the convergence control parameters of the auxiliary function. For determination of optimal values of constants we use method of least square and collocation method. We use Mathematica 7 for symbolic computation. Most of the work presented in chapters 2, 3,4,5 and 6 of this thesis has been published in 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.
Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

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