قرآن کا اسلوب دعوت اور معاشرے پر اس کے اثرات

Human is a combination of a body and soul, in which body is nurtured by means of energy that is present around the world, but regarding soul, he has not provide nourishment in this world. For his soul’s nourishment, Allah has revealed prophets from Adam Alehi Salaam to Muhammad Sallallaho Alaehi Wasallam with books, these books are with different methodologies, as creator knows that there is no definite way which can appeal human mind and soul. God manifested the color of love in psalm through songs, instructions have been given through stories in Touraat and Bible has proven it be the best model of proverbs. Quran which is the last revelation of God, combined all above ways to open the door to soul. It has reflection of David’s songs, Glory of Moses and divine glance of Maseeh (P.B.U.T) it has restrictions of Sharia laws and spirituality. Aim of Holy Quran is just not to conquer the opponent by logical argument but it open his heart for right path - for this reason the book itself explained way to call the people towards Islam. It says call people to the way with wisdom and fair of exhortation and reason with them in the best possible way. These rules are only effective when followed with love and well-wishing which is shown through soft and lenient tone. In this article, I have discussed concept and need of Dawat, basic pillars and etiquettes in the light of Holy Quran and Hadith.

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.