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Subdivision Schemes and Their Applications to Solve Differential Equations

Thesis Info

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External Link

Author

Ejaz, Tehmina

Program

PhD

Institute

The Islamia University of Bahawalpur

City

Bahawalpur

Province

Punjab

Country

Pakistan

Thesis Completing Year

2016

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/8175/1/Ph.%20D.%20Thesis%20By%20%20Syeda%20Tehmina%20Ejaz.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727411653

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Subdivision schemes are important for the generation of smooth curves and surfaces through an iterative process from a finite set of points. The subdivision schemes have been considered well-regarded in many fields of computational sciences. In this dissertation, we have used subdivision schemes for the numerical solution of different types of boundary value problems. In literature three methods such as spline based methods, finite difference methods and finite element methods are commonly used to find the numerical solution of boundary value problems. Subdivision based algorithms for the numerical solution of second order boundary value problems have also been used in the literature. In this dissertation, we develop subdivision based collocation algorithms for the numerical solution of linear and non linear boundary value problems of order three and four. Subdivision based collocation algorithms for the solution of second and third order singularly perturbed boundary value problems are also presented in this dissertation. These algorithms are developed by using basis functions of subdivision schemes. Convergence analysis of these collocation algorithms are also discussed. Accuracy and efficiency of the developed algorithms are shown through comparison with the existing numerical algorithms.
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مولانا صفی الرحمن مبارکپوری

مولانا صفی الرحمان مبارک پوری
بہ روز جمعہ یکم دسمبر ۲۰۰۶؁ء کو مرکزی جمعیۃ اہل حدیث ہند کے سابق امیر اور صاحب الرحیق المختوم مولانا صفی الرحمان مبارک پوری نے داعی اجل کو لبیک کہا، اناﷲ وانا الیہ راجعون۔
ضلع اعظم گڑھ میں مبارک پور پارچہ بافی کی صنعت کے لیے ایک مشہور قصبہ ہے جو علمی و تعلیمی حیثیت سے بھی ممتاز ہے اور یہ بعض بڑے علما و مصنفین کا مولد و مسکن بھی رہا ہے، مبارک پور سے متصل جانب شمال میں حسین آباد کی بستی میں مولانا صفی الرحمان صاحب ۱۹۴۲؁ء میں پیدا ہوئے۔
انہوں نے جامعہ فیض عام مؤ سے درس نظامی کی تحصیل کی اور اسی دوران الٰہ آباد بورڈ کے امتحانات مولوی اور عالم بھی پاس کئے، تعلیمی مرحلہ ختم کرنے کے بعد کئی مدارس میں تدریسی خدمات انجام دیں، ۱۹۷۱؁ء کی ہند و پاک کی جنگ کے زمانے میں وہ جامعتہ الرشاد سے وابستہ تھے، اس زمانے میں دارالمصنفین اکثر آتے اور کتب خانے سے استفادہ کرتے، مجھ سے اور مولوی ابوعلی عبدالباری صاحب مرحوم سے بہت بے تکلف ہوگئے تھے اور مختلف علمی ،دینی اور قومی و سیاسی مسائل پر گفتگو کرتے، اس سے ان کی ذہانت، قوت گویائی، اچھی صلاحیت اور مسائل حاضرہ سے باخبری کا انداز ہوتا، ہونہار بروا کے چکنے چکنے پات۔
مگر جامعۃ الرشاد سے ان کا تعلق بہت کم عرصے تک رہا اور بالآخر وہ اپنی اصلی جگہ پہنچ گئے یعنی جامعہ سلفیہ بنارس میں درس و تدریس کی خدمت انہیں تفویض کی گئی، یہاں ان کی مخفی صلاحیتیں جلاپانے لگیں، تقریر و خطابت کا ملکہ تو پہلے ہی سے ان میں نمایاں تھا، یہاں آکر قلم نے بھی گل کاریاں شروع کیں تو جامعہ کے ماہانہ رسالہ ’’محدث‘‘ کی ادارت کی ذمہ داری ان کو سپرد کی گئی جسے انہوں نے حسن...

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Shaykh Muhammad Nasiruddin Albani is known as the famous scholar of the twentieth century AD. He served in Hadith for almost 60 years. He has also some particularities in the hadith’s research in which he apposed a lot of scholars. The most important of them is that he has said that some Ahadith of Sahih Bukhari and Sahi Muslim are weak. Similarly, in contrast to the previous muhaddiseen, some weak traditions have said correct and some reliable narrators as weak. Apart from this, there are two particularities of him that are very important in the research world. One is that he has explored many of unknown Ahadith and secondly he has divided the books of Hadith into two parts; weak and accurate. Some detail of these particularities is presented in this article.

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