معاصر خانقاہی نظام میں خانقاہ سراجیہ کے امتیازات

Mawlānā abu Sa'ad Ahmed Khan's sincerity, piety, adherence to the sunnah of the prophet and simplicity in his lifetime made this monastery a unique city in the subcontinent and a centre of universal growth and guidance. Gave after him Mawlānā Abdullah Ludhianvi, Khwaja Khan Muhammad and Khwaja Khalil Ahmad continued his mission. In addition to reforming the human population, the shuyūkh of this monastery has been following the sunnah of the prophet, reforming society, promoting education, preserving the belief at the end of prophethood, patronage of madrassas and religious parties, charitable work and promoting Naqshbandiyya.  And the emperors and officials have done their best to play their role in the implementation of the Islamic system and the establishment of the justice system in the country. Mashaikh of the monastery broke the intellectual statement of the religious schools by imparting practical training, Self-purification, spiritual asceticism, religious support, prophetic politics and modern insights. On the other hand, volunteer religious services and selfless sacrifice to bring the right path to the people, as well as the public meetings, strong character and perseverance religious influenced by source. Through his voluntary religious services and selfless sacrifices, he tried to bring them to the right… In this way, these gentlemen addressed the masses through Zikr, strong character and religious perseverance, influenced by source.

Subdivision Schemes and Their Applications to Solve Differential Equations

Subdivision schemes are important for the generation of smooth curves and surfaces through an iterative process from a finite set of points. The subdivision schemes have been considered well-regarded in many fields of computational sciences. In this dissertation, we have used subdivision schemes for the numerical solution of different types of boundary value problems. In literature three methods such as spline based methods, finite difference methods and finite element methods are commonly used to find the numerical solution of boundary value problems. Subdivision based algorithms for the numerical solution of second order boundary value problems have also been used in the literature. In this dissertation, we develop subdivision based collocation algorithms for the numerical solution of linear and non linear boundary value problems of order three and four. Subdivision based collocation algorithms for the solution of second and third order singularly perturbed boundary value problems are also presented in this dissertation. These algorithms are developed by using basis functions of subdivision schemes. Convergence analysis of these collocation algorithms are also discussed. Accuracy and efficiency of the developed algorithms are shown through comparison with the existing numerical algorithms.