دراسة الرتبة النحوية في الجملة القرآنية

The Syntactical Study of the Quranic Phraseology Arabic language renders primal focus on syntactical placement of words in a sentence id est each constituent of the sentence contains some specific placement which connotes the propriety of the sentence and it plays a vital role in its structural unity. It ought to be kept in mind that ancient syntacticians had unanimously concluded the primal role of specific placement. They highlighted its various forms as in some conditions constituents of a sentence can be replaced from its specific structural placement, for instance, object is placed in place of subject as in “ jaa ni alqom”( جاءني القوم) the people came to me. While in some other cases and conditions such replacement is not admissible and if such re-structure is made, it will dilute the connotation, for instance, the positions of conjunctive pronoun before the principal clause, adjective with noun, possessive noun with the noun-possession and the conditional clause with the sub-ordinate clause are not admissible otherwise all these re-placement of the constituents in a sentence will cause the deformation of structure and implications.

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.