دار العلوم دیو بند کی تعلیمی و عصری خدمات کا تنقیدی مطالعہ

Purpose of the study was to reflect great contributions of Dar ul Uloom Deouband. After the end of Independence War 1857, three factors endangered the Muslims of India religiously and educationally. Firstly, the Christian missionaries who thought that after the political downfall Muslims would convert themselves to Christianity. Secondly, the missionaries were proclaiming blasphemy about Islam and the Holy Prophet Muhammad Sallalaho Alaha Wasalam. In this regard, William Mure wrote a notorious blasphemous book about which Sir Syed said, “Alas! We like to die.” Thirdly, in these circumstances the doubts of Muslims were increasing that Muslim may not be converted to Christianity but it may create hatred from Islamic ideology.  Just to cope up with these dangers, various educational movements came into being; one of them is Deouband Movement. As a result of the efforts by Dar ul Uloom Deouband, Muslims were able to save their Din and eman.

Haar Wavelet Approach for Numerical Solution of Ordinary, Partial and Fractional Differential Equations With Delay

In this thesis, the main emphasis is on collocation technique using Haar wavelet. A new method based on Haar wavelet collocation is being formu- lated for numerical solution of delay differential equations, delay differential systems, delay partial differential equations and fractional delay differential equations. The numerical method is applied to both linear and nonlinear time invariant delay differential equations, time-varying delay differential equa- tions and system of these equations. For delay partial differential equations two methods are considered: the first one is a hybrid method of finite differ- ence scheme and one-dimensional Haar wavelet collocation method while in the second method two-dimensional Haar wavelet collocation method is ap- plied, and a comparative study is performed between the two methods. We also extend the method developed for delay differential equations to solve nu- merically fractional delay differential equations using Caputo derivatives and Haar wavelet. Here we consider fractional derivatives in the Caputo sense. Also we designed algorithms for all the new developed methods. The imple- mentations and testing of all methods are performed in MATLAB software. Several numerical experiments are conducted to verify the accuracy, ef- ficiency and convergence of the proposed method. The proposed method is also compared with some of the existing numerical methods in the literature and is applied to a number of benchmark test problems. The numerical re- sults are also compared with the exact solutions and the performance of the method is demonstrated by calculating the maximum absolute errors, mean square root errors and experimental rates of convergence for different number of collocation points. The numerical results show that the method is simply applicable, accurate, efficient and robust