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Analytical Solutions to Some Nonlinear Boundary Value Problems Arising in Applied Mathematics

Thesis Info

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Author

Fiza, Mehreen

Program

PhD

Institute

Abdul Wali Khan University

City

Mardan

Province

KPK

Country

Pakistan

Thesis Completing Year

2019

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/11542/1/Mehreen%20Fiza%20%20maths%202019%20awk%20mardan%20prr.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676725499890

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In this thesis, we use the Optimal Homotopy Asymptotic Method (OHAM), Differential Tranform Method (DTM), Multistage Optimal Homotopy Asymptotic Method (MOHAM), Adomian decomposition method (ADM) and Homotopy analysis method (HAM) for the solution of nonlinear initial and boundary value problems for ordinary and partial differential equations. The obtained results are compared with the results obtained from these methods and numerical results. These method do not required the linearization and discritization techniques like numerical methods andestablished better accuracy at low order approximation and its accuracy increases with increase in approximation orders; it uses a flexible auxiliary function that control the convergence of the solution and convergence region can easily be adjusted. Moreover, the procedure of these method are simple, well defined, and can easily be used the recursive relations explicitly. Except from the application of these methods, we have formulated some fluid problems and its solutions have been done. The physical interpretations of the parameters are discussed in detail. The conclusion of each model is given at the end of each chapter. The convergence regions for each problem have been mentioned graphically and the convergence is discussed. Also we have developed a new scheme for namely MOHAM which gives better accuracy not even for small domain problems but works very well for large domain boundary value problems. The implementation of this scheme is almost simple as the optimal homotopy asymptotic method.To shows its effectiveness we have used it to different bench mark problems from literature and compare the results with those obtained by other method. Fordeterminationofoptimalvaluesofconstantswe usemethodofleastsquareand collocation method for OHAM and MOHAM. For HAM h curves determine the convergence region and rate of convergence. We use Mathematica 9 for symbolic computation. Most of theworkpresentedinchapters2, 3,4,and5ofthisthesishasbeen publishedin different well reputed international journals and the remaining are submitted for possible publications. The details of published/accepted/submitted are included in the list of publications.
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ملا طاہر سیف الدین

ملا طاہر سیف الدین
گذشتہ دو مہینوں میں مسلمانوں کے دو بڑے قومی حادثے ہوئے، ۵؍ نومبر کو داؤدی بوہرون کے امام ملا طاہر سیف الدین نے انتقال کیا، ان کی ذات جامع صفات تھی، بڑے ذی علم، دیندار، فیاض و مخیر اور وسیع القلب تھے، دینی علوم پر ان کی نگاہ بہت وسیع تھی، اس لحاظ سے وہ ہندوستان کے ممتاز علماء میں تھے، صاحبِ قلم بھی تھے، عربی میں ان کی کئی تصانیف ہیں، انھوں نے اپنے دور میں نہ صرف اپنے فرقہ کی بڑی تعلیمی و اقتصادی خدمت کی بلکہ دوسرے اسلامی فرقوں کے ساتھ بھی ان کا سلوک روادرانہ و فیاضانہ تھا، اور ان کو ایک دوسرے کے قریب لانے کی کوشش کی، مسلم یونیورسٹی کے تو چانسلر ہی تھے، اس کو وقتاً فوقتاً بڑی بڑی رقمیں دیتے رہتے تھے، دارالمصنفین کی جوبلی کے موقع پر اس کو بارہ ہزار کا عطیہ دیا، اس لیے ہر فرقہ کے مسلمانوں میں عزت و وقعت کی نظر سے دیکھے جاتے تھے، اﷲ تعالیٰ ان کے حسنات کے طفیل میں ان کی مغفرت فرمائے، دارالمصنفین اس حادثہ میں ان کے لائق جانشین ملا برہان الدین کا شریک غم ہے اور دعا ہے کہ خدا ان کو ان کے باعظمت والد کے نقش قدم پر چلنے کی توفیق عطا فرمائے۔ (شاہ معین الدین ندوی، دسمبر ۱۹۶۵ء)

 

ذبح سے پہلے عمل تدویخ اور معاصر فقہی تحقیقات

Stunning is the process of rendering animals immobile or unconscious, with or without killing the animal, when or immediately prior to slaughtering them for food. In modern slaughterhouses a variety of stunning methods are used on livestock. Methods include: Electrical stunning, Gas stunning, Percussive stunning. There are three opinions of Islamic scholars about stunning. Those scholars; who do not allow stunning at all; are of the view that the method of rendering animals unconscious before slaughter is against the shairah method and Sunnah, and it is Makrooh e Teḥreemi. Before slaughtering, if an animal died due to stunning, then that animal is carcass and is not allowed to be eaten. But, if before slaughter, ḥayat e Mustaqirrah is present in animal and it is slaughtered in that condition then it is permissible to eat it. Certain scholars allow stunning in certain situations with some terms and conditions. The decisions of Mjam e Faqhiyyah of modern age are also based on conditional permission. Moreover, Mufti Muḥammad Taqi Usmani, Dr. Wahabah  Zoḥaili and Abdul Aziz Bin Baaz agree with conditional permission, while some other scholars allow all types of stunning without any condition; Mufti Muḥammad Abduho and his pupil Allamah Rasheed Raza Miṣri agree with later opinion.

Risk Management Issues in Coventional and Islamic Banking in Pakistan

The basic thrust of current study is to measure the magnitude and to gauge the severity of financial risk on profitability associated with the Islamic and conventional banking in Pakistan. To realize the magnitude and enormity of financial risk the credit, liquidity, interest rate and market risks are considered as major constituent of risk management practices. The magnitude of credit risk was calculated through conventionally recognized quantitative models (Z-Score, Altman Z-score, NPL ratio and Distance to Default and Default Probabilities for Black Schole Merton’s Model) whereas, the enormity of liquidity risk calculated through ratios including; cash and cash equivalent to total assets, investment to total assets and provision for net advances to total assets. Likewise, interest rate risk was computed by applying historical Gap Identification Model. The market risk was estimated through Value at Risk (VaR) Model at 90%, 95% and 99% confidence intervals. To gauge the combined effect of risk management practices on profitability and to realize the appropriate applicability of fixed or random effect model the Hauseman test was applied. The computed results of credit risk found Islamic banks hold more risk whereas the probability of bankruptcy in near future felt more in conventional banks relative to Islamic banks. The overall findings of liquidity risk revealed conventional banks possess a sound liquidity arrangement than Islamic banks. The sensitivity of interest rate on the volatility of interest income and the variability of liabilities as compared with assets were bit high among conventional banks. By and large, the calculated results of market risk inferred the volatility and potential to loss investment remained high in Islamic banks. Though, severity of financial crisis-2008 profusely hit the profitability of both banking systems but the Islamic banks felt more aggressively. The enormity of the credit risk accentuate management of the Islamic banks to give more emphasis on the credit risk whereas, the State Bank of Pakistan will have to keenly think on the changing paradigm of the interest rate sensitivity on the conventional banks and formulate unified strategies which may widely adopted by the conventional banks and prevent from future trauma.