Impacts of Psychological and Domestic Violence On Women in Pakistan: Problems & Solutions in the Light of Islamic Teachings

Since the creation of woman, she faces many problems in her life. Different societies have their own customs and traditions. And woman faces problems regarding them. Pakistani society has its own influence and civilization which causes many problems of women. In these traditions, one of the bad behaviors is, marriage of woman on wrong time i.e. Late marriage or early time marriage. In the result, at least, she faces Problems regarding dowry, Joint family system, Family disintegration, Childlessness, Propensity to violence, Effects of husband remaining alone from wife etc. On the basis of social divisions in Pakistani family system and depiction of woman issues having effects on herself, the significant and their mediation is very necessary, too. Many of these problems has Psychological impacts on woman in her domestic life. In Pakistani society where woman faces domestic and family problems, there economic problems too pester her which include greed for riches and lack of them both pester her psychologically. In this paper, above mentioned problems of women in Pakistani society has been discussed in the light of Islamic teachings.

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.