عصمت أنبیاء سے بظاہر متعارض صحیحین کی بعض أحادیث کا علمی جائزہ

Abstract: Prophets and Messengers have the holiest status amongst Allah’s creation. They are the caliph of Allah in the world. Allah’s characteristics which can be present in a human after Him are present in Prophets and Messengers. That’s why Umma believes in their innocence. The purpose of their prophecy is guidance and breeding of the humanity. One of the most effective tool for breeding is that the breeder must possess the qualities which bring people closer to him. For this reason، Prophets/Messengers should be free and away from all hateful and bad habits. Some hadiths from the Hadith books are seen which appear inappropriate and against prophets grace and honor. That’s why some people have rejected those hadiths for being against prophets’ honor. In this article، we will discuss the hadith present in Sahih Bukhari and Sahih Muslim which appear against the honor of the prophets.

Numerical Solution of Boundary and Initial Boundary-Value Problems Using Polynomial and Non-Polynomial Spline Functions Method

The boundary and initial boundary value problems have always played a vital character in the fields of science and technology. Different numerical techniques are used to obtain numerical approximations of such problems. We present and illustrate novel numerical techniques for the numerical approximations of higher order boundary and initial boundary value problems. The numerical techniques derived in this research work are based upon the fact of employing polynomial cubic spline (PCS) scheme and non polynomial cubic spline (NPCS) scheme in conjunction with the decomposition procedure. In the case for ordinary differential equations, the decomposition procedure is used to reduce the higher order boundary value problems (BVPs) into the corresponding system of second order boundary value problems. Then PCS and NPCS schemes are constructed for each second order ordinary differential equation. The first order derivatives are approximated by the central finite differences of(ℎ ). For partial differential equations, the second order time derivatives are decomposed into the first order derivatives. The process of decomposition generates a linear system of partial differential equations, where the first order time derivatives are approximated by the central finite differences. The performance of the new derived schemes is illustrated by numerical tests that involve comparing numerical approximations with analytical solutions on a collection of carefully selected problems from the literature. These problems range from those involving higher order ordinary differential equations, for example, fifth, sixth, seventh, twelfth, and thirteenth order ordinary differential equations and partial differential equations, like fourth order parabolic equations, one dimensional hyperbolic telegraph equations, and one dimensional wave equations. In addition, Adomian decomposition method is used to construct the boundary conditions for the solution of fourth order parabolic equations.