جو مہرباں تھے مرے اب وہ مہرباں نہ رہے
خفا کسی سے کبھی ایسے آسماں نہ رہے
جو وقت بدلا تو پھر لوگ بھی بدلنے لگے
جو راز داں تھے کبھی پھر وہ رازداں نہ رہے
ہر ایک شخص گیا ہٹ مقام سے اپنے
نہ پیر پیر رہے وہ جواں جواں نہ رہے
ستم ظریف نے کہہ کر یہ آگ لگوائی
کسی بھی طور مرا باقی آشیاں نہ رہے
وہ خوش نصیب ہے خوش بخت جس کا تائب جی
زمانہ لاکھ رہے یار بدگماں نہ رہے
Allama Ghulam Rasool Saeedi was a great Muslim scholar of Pakistan. He served the Muslim Ummah more than 79 years. He taught Quran & sunnah for more than five decades. He made his great research work on Quranic Tafaseer, Hadith literature and Islamic jurisprudence. One of his distinction is his work on difference of opinion with the scholar of past and present also. As we know difference of opinion is the basic component of human nature and instinct. Allama Saeedi worked on this difference in his work in honorable manners and ethics. He tried to minimize the sectarianism. This article aims to discuss the contribution of Allama saeedi in this regard.
The development of nonlinear science has grown an ever-increasing interest among scientists and engineers for analytical asymptotic techniques for solving nonlinear problems. Finding solutions to linear problems by means of computer is easier nowadays; however, it is still difficult to solve nonlinear problems numerically or theoretically. The reason is the use of iterative techniques in the various discretization methods or numerical simulations to find numerical solutions to nonlinear problems. Almost all iterative methods are sensitive to initial solutions; hence, it is very difficult to obtain converging results in cases of strong nonlinearity. The objective of this dissertation is to use Optimal Homotopy Asymptotic Method (OHAM), a new semi-analytic approximating technique, for solving linear and nonlinear initial and boundary value problems. The semi analytic solutions of nonlinear fourth order, eighth order, special fourth order and special sixth order boundary-value problems are computed using OHAM. Successful application of OHAM for squeezing flow is a major task in this study. This dissertation also investigates the effectiveness of OHAM formulation for Partial Differential Equations (Wave Equation and Korteweg de Vries). OHAM is independent of the free parameter and there is no need of the initial guess as there is in Homotopy Perturbation Method (HPM), Variational Iteration Method (VIM) and Homotopy Analysis Method (HAM). OHAM works very well with large domains and provides better accuracy at lower-order of approximations. Moreover, the convergence domain can be easily adjusted. The results are compared with other methods like HPM, VIM and HAM, which reveal that OHAM is effective, simpler, easier and explicit.