برصغیر میں غیر مسلم اہل قلم کے بزبان اردو تراجم و تفاسیر قرآنی

Islamic literary legacy is diverse and multidimensional in Sub-continent despite its being prone to religious b and the issue of migration integral part of Islamic literary legacy is the Quranic translations & interpretations. The main aspect of these translations & interpretations are the endeavors put forward by Muslim as well as non-Muslim scholars. Keeping in view the endeavors translations & interpretations of Quran, the non-Muslims minorities of sub-continent can be divided into two groups. The first group of part is based on the followers of Judaism, Parsee, Buddhist, Sikhism, Jainism and idols of Kalash whose translations and interpretations is not well known. Whereas, the second group endure Christians, Hindus and Qadyanis. Christians and Hidus consider Quran as non-revealed. Since the style of their interpretations is based on criticism and rejection in aggressive manner. Whereas the interpretations by Qadyanis are focused on religious polarized beliefs and ideologies taking into considerations Quran as revealed. That’s why Qadyanis interpretations are not accepted in Muslim community. The criticism by non-Muslims writers has resulted in rational approach for study of Quran instead of tendency based on esteem among Muslim. This paper represents aforementioned non-Muslims services regarding Quranic Interpretations and Translations which are distinguished in Muslims Interpreters.

Meshfree Methods for the Numerical Solutions of Partial Differential Equations

In this dissertation, meshfree (meshless) methods using meshless shape functions are proposed for the numerical solutions of partial differential equations (PDEs). These PDEs have either integer or fractional order time derivatives. Weighted θ-scheme (0≤θ ≤1) is used for time discretization of integer case, whereas, for fractional case, the same discretization scheme is combined with a simple quadrature formula. For space (spatial) discretization we used meshless shape functions owing Kronecker delta function property. These shape functions are obtained viapointinterpolationapproachandradialbasisfunctions(RBFs). Finallywiththehelpofcollocationmethodthe given PDE reduces to system of algebraic equations, which are then solved via LU decomposition in iterations. For the proposed numerical scheme, stability analysis is carried out theoretically and computational examples are provided to support the analysis. The proposed scheme has been tested via application to several concrete and benchmark problems of engineering interest. ApproximationqualityandaccuracyofcomputedsolutionsaremeasuredusingL∞, L2 andLrms discrete errornorms. Efficiencyandorderofapproximationoftheproposedschemeinspaceandtimeareanalyzedthrough variation of number of nodal points N and time step-size δt. The documented results, in the form of tables and figures, reveal very good agreement to true solutions as well high accuracy to earlier proposed technique available in the literature. In RBFs, the presence of shape (support) parameter c∗ plays a crucial role. Accuracy of the RBFs based scheme can be improved via proper selection of this parameter. For this purpose, an automatic optimal shape parameter selection algorithm is proposed. To check effectiveness and automatic (adaptive) nature of this algorithm in RBFs approximation method, time fractional Black-Scholes models have been solved. It has been noted that the proposed algorithm worked well and gives excellent accurate solutions for various fractional order time derivatives. The RBFs approximation (Kansa) method results in dense ill-conditioned matrix. For the treatment of this issue weproposeahybridRBFs(HRBFs)approximationmethod. Byextendingthisidea, anadaptive(automatic)algorithm is proposed for optimal parameters selection in HRBFs. For validation, again time fractional Black-Scholes models are reconsidered. Simulations revealed acceptable accurate solutions in hybrid RBFs method too. Along with that significant reduction in condition number of the resultant matrix is observed up to several manifold. Hence, HRBFs method can be seen as an alternative remedy for curing ill-conditioning in usual RBFs method. Computer simulations have been carried out via MATLAB R2013a on a personal laptop with configuration, Processor: Intel(R) Core(TM) i5-5200U CPU @ 2.20GHz 2.20GHz, RAM: 4.00 GB, System type: 64-bit Operating System, x64-based processor.