حافظ احمد علی خان شوق
یہ خبر افسوس کے ساتھ سنی جائیگی کہ رامپور کے مشہور علم دوست فاضل اور وہاں کے مشہور شاہی کتب خانہ کے سابق ناظم اور متعدد کتابوں کے مترجم و مصنف حافظ احمد علی خان صاحب شوقؔ نے اوائل رمضان المبارک ۱۳۵۲ھ میں تقریباً پینسٹھ اور ستر کی عمر کے درمیان میں انتقال فرمایا، مرحوم نہایت بااخلاق، بامروت، علم دوست اور صاحب کمال تھے، قلمی اور نادر کتابوں کے خاص ماہر تھے، معارف کے ناظرین کبھی کبھی ان کی تحقیقات سے مستفید ہوا کرتے تھے، ان کی سب سے بہتر کتاب تذکرہ کاملین رام پور ہے، اﷲ تعالیٰ غریق رحمت کرے۔ (سید سلیمان ندوی،جنوری ۱۹۴۳ء)
This is the well-known fact that ebadat are the most important articles of Islam. Ebadat bring many spiritual and material benefits to worshipers (Muslim), and this included peace of mind and satisfaction of heart. This point is discussed in this article in detail with reference to the relevant verses of Quran and Prophetic Sunnah in the light of Tafaseer perspectives. A person who bow to Allah Almighty sincerely, he offers prayers in time and pay Zakat to get the Will of Allah, he becomes a great man who is blessed with peace of mind as being agree in every condition with believing in Allah SWT being as satisfaction for him and makes him free from mental tension and anxiety. In the view of Quran e Kareem, the main reason for giving details of the rewards and benedictions of the Paradise is to develop satisfaction within the hearts of the worshipers. It is observed that only the way of attaining real peace of mind and satisfaction of heart is to be punctual and regular in offering prayers and paying zakat sincerely realization in the true sense.
Higher-order numerical techniques are developed for the solution of (i) homogeneous heat equation u t = u xx and (ii) inhomogeneous heat equation u t = u xx + s(x, t) subject to initial condition u(x, 0) = f (x), 0 < x < 1, boundary condition u(0, t) = g(t)0 < t ≤ T and with non-local boundary condition(s) (i) b 0 u(x, t)dx = M (t) 0 < t ≤ T, 0 < b < 1 (ii) u(0, t) = (iii) u(1, t) = 1 0 φ(x, t)u(x, t)dx + g 1 (t), 0 < t ≤ T and 1 0 ψ(x, t)u(x, t)dx + g 2 (t), 0 < t ≤ T as appropriate. The integral conditions are approximated using Simpson’s 1 3 rule while the space derivatives are approximated by higher-order finite difference approxi- mations. Then method of lines, semidiscritization approach, is used to trans- form the model partial differential equations into systems of first-order linear ordinary differential equations whose solutions satisfy recurrence relations in- volving matrix exponential functions. The methods are higher-order accurate in space and time and do not require the use of complex arithmetic. Parallel algorithms are also developed and implemented on several problems from lit- erature and are found to be highly accurate. Solutions of these problems are compared with the exact solutions and the solutions obtained by alternative techniques where available.