Legitimacy of Imprisonment as a Punishment in Sharīa

Throughout known human history, incarceration has been a prevailing practice. Regardless of the nature of the crime, imprisonment is now a widespread phenomenon globally. In Pakistan, as in many other states, detention is employed for a wide range of offenses, including instances where Islamic capital punishments are substituted with imprisonment. The adverse impacts of imprisonment are not limited to the individual offender; rather, they extend to the well-being of the offender's family and the broader society. Furthermore, the efficacy of imprisonment is questioned concerning its purported benefits in terms of reformation, retribution, and deterrence, with an examination revealing potential limitations in achieving these objectives. Considering the aforementioned issues, it is important to explore whether it is according to Islamic law or not? After analyzing all causes and aspects of detention given in the Prophetic time and Rashidun caliphate, it is concluded that in those times, imprisonment was just practiced till the decision taken for the criminal and then, one might set free or granted any hadd or ta‘zīr punishment. Subsequently, the individual could either be released or subjected to specific hadd or ta‘zīr punishments. In Shari'ah, permissible punishments include confining the offender to their residence or banishing them from the locality, with the provision for the latter to be accompanied by their family. Crucially, the absence of a concept of prolonged imprisonment within Sharīa’s code of crimes and penalties underscores the contention that imprisonment is perceived not merely as a punitive measure but as a severe crime against humanity.  This raises questions about the effectiveness of Pakistan's criminal justice system, suggesting that a more tailored and nuanced approach, considering individual circumstances, may be more operative. Keywords: Juristic Approach to Imprisonment, Imprisonment in Islam, detention in Islamic law, incarceration.

New B-Spline Approximations for Numerical Solution of Initial and Boundary Value Problems

In this work, new cubic, quartic and quintic B-spline approximations are proposed for approximate solution of initial and boundary value problems. The error analysis of these new approximations has been executed, which affirms their uniform convergence in entire spatial domain. The numerical algorithms based on B-spline functions assembled with new approximations are developed for numerical solution of second, third and fourth singular initial and boundary value problems. The L''Hospital''s Rule has been utilized for removal of singularities. The non-linear equation is first changed into a system of linear equations with the help of quasi-linearization technique and then solved by a modified form of well known Thomas algorithm. Moreover, numerical schemes based on usual finite difference formulation and new B-spline approximations are also presented for numerical solution of three non-linear mathematical models named as Klein-Gordon equation, Korteweg-de Vries equation and Kuramoto-Sivashinsky equation. The finite difference formulation is used for temporal discretization, whereas, new B--spline approximations based on Crank--Nicolson scheme have been used to interpolate the solution in space direction. The proposed numerical schemes are proved to be unconditionally stable subject to the Von-Neuman stability analysis. In order to corroborate this work, several test examples have been considered and the computational outcomes are compared with existing numerical techniques. It is revealed that by virtu of simple and straightforward implementation, our new B-spline approximations produce more accurate outcomes as compared to other variants on the topic.