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Optimal Homotopy Asymptotic Method to Solution of Partial Differential Equations

Thesis Info

Access Option

External Link

Author

Nawaz, Rashid

Program

PhD

Institute

University of Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2014

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2356/1/2945S.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726813857

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Nonlinear Differential equations are of major importance in different fields of science and engineering. For complicated nonlinear problems exact solutions are not available and alternate way is to use numerical methods, Iterative methods or analytical techniques of perturbation. Numerical methods use discretization a have slow rate of convergence. Iterative methods are sensitive to initial conditions and in case of high nonlinearity they do not yield converged results. In perturbation methods small parameter is applied on the equation and hence cannot be applied for high nonlinear problems as they do not have small parameter. One of domain type methods is known as OHAM. This method is free from small parameter assumption and do not need the initial guess. The proposed method provides better accuracy at lower-order of approximations. Moreover the convergence domain can be easily adjusted. In this thesis OHAM is implemented for solution linear and nonlinear tenth order ODEs. Then its effectiveness and generalization is shown to a nonlinear family of PDEs, including Burger, Fisher, Burger’s–Huxley, Burger’s–Fisher, MEW and DGRLW equations. The results of the proposed method are compared with that of DTM, VIM, ADM, HAM and HPM, which reveal that OHAM is effective, simpler, easier and explicit. Apart from application to PDEs, OHAM is applied to couple system of PDEs. The coupled WBK, ALW, MB systems are used as test examples and results are compared with those obtained by HPM. OHAM is implemented to DDEs as well, and solution of MKdV lattice equation is presented for the illustration of proposed technique. The results are compared with HAM and HPM. In all cases the results obtained by OHAM are in close agreement with the exact solution and reveal high accuracy.
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اردو کے اہم مدونین (امتیاز علی عرشی)

اردو کے اہم مدونین (امتیاز علی عرشی)
امتیاز علی خان عرشی کا امتیاز یہ ہے کہ انہوں نے اردو ادب کو تحقیق کے آداب و رموز سے آشنا کیا۔ تحشیہ و تدوین کا معیار قائم کیا اور اپنی تحقیقی کاوشوں سے ادب کو بیش بہا تصانیف سے روشناس کروایا۔ان کی تدوین، تحقیق کے تازہ واردان کی رہبری اور رہنمائی کرتی اور انہیں اس فن کے اصولوں سے آگاہ کرتی ہے۔بہت سی کتابوں کو عرشی نے نئی زندگی عطا کی اور اردو تدوین کو اعتبار بخشا۔امتیاز علی عرشی ۸ دسمبر۱۹۰۴ء کو رام پور میں پیدا ہوئے۔ملازمت کی بھی تو علم و ادب سے وابستہ رہے۔ فروری ۱۹۸۱ء میں رام پور میں انتقال کیا۔آپ کی اہم تصنیف مندرجہ ذیل ہیں:
• مکاتیب غالب • نظام نامہ
• ترجمہ مجالس رنگین • انتخاب غالب
• نادرات شاہی از شاہ عالم • سلک گوہر از انشاء
• کہانی رانی کیتکی کی از انشاء
دیوان غالب:
تحقیق میں امتیاز علی عرشی کا خاص کارنامہ ان کی قابل قدر تدوین و ترتیب ہے۔ اختلافات نسخ، جعلی نسخوں ، تصحیح متن، حوالوں کی جانچ پڑتال اور تحقیقی مواد کی فراہمی کا ان میں ایک خاص سلیقہ موجود ہے۔ غالبیات کے ماہر کی حیثیت سے ان کے تحقیقی اور علمی کارنامے ناقابل فراموش ہیں۔غالبیات کے ماہر ہونے کے علاوہ امتیاز علی عرشی نے دوسرے موضوعات پر بھی قلم اٹھایا ہے۔ غالب کے علاوہ عرشی نے انشاء اور سعادت یار خان رنگین کے کلام اور ان کے ادبی اکتباسات سے بھی دل چسپی لی ہے۔عرشی کے علم کا دائرہ بہت وسیع تھا۔انہوں نے تاریخ سے بھی دل چسپی لی اور اس کے پس منظر میں ادب کی نشوونما کا جائزہ لینے کی کوشش کی ہے۔
حافظ محمود شیرانی اگر اردو تحقیق کے معلم اول ہیں تو معلم ثانی صرف اور صرف امتیاز علی خان...

The Dress Code for Muslim Women: A Linguistic Analysis of the Qurānic Verses and the Prophetic Traditions

It is not uncommon to find cases of Muslim women being harassed or bullied in many of the Muslim-minority countries because of their dress. These Islamophobic attacks, unfortunately, are not merely conducted by radicalised individuals; but the subjugation of the rights of Muslim women also comes from institutional bodies and governments. Secular nations, such as France, Germany, Italy, Belgium, Netherlands, Bulgaria, Switzerland, USA, UK, Canada, China, and Russia have either imposed restrictions on Muslim women regarding their dress code. They see veil as a non-acceptance of progressive or cumulative values which is unsurprisingly not welcomed by the Muslim community. In such environment, it is inevitable for the Muslims to understand what the Qur’ān and Sunnah really say about the dress code for Muslim women in order to explain what their religion really requires from them and to communicate it appropriately to the government officials, journalists, politicians, and other relevant stakeholders. It is also essential from the perspective of segregating cultural aspects from the religious aspects. Many of the commonly used words for the dressing of Muslim women are more rooted in culture than the religion. It is accordingly vital to understand what the Qur’ān and Sunnah really command about the women dressing and how it has been interpreted in various Islamic societies and cultures. This paper accordingly presents an analysis of all the relevant Qur’ānic verses and the prophetic traditions (from the 6 most renowned books of ahadith). The linguistic analysis employed in this paper results in the identification of items of dress that were worn by Muslim women to safeguard their modesty during the times of Prophet Muhammad (ﷺ). The same principles are relevant for today’s age and time and the Muslims can use those guidelines to delineate cultural practices from the religious injunctions.

A Topology-Awareload Balancing Scheme in Data Center Networks

Datacenter networks are playing vital role to accommodate huge amount of data transmission such as in Giga/Tera bytes on multiple links. With this inevitable data transmission, some uncertainties like dynamic traffic behaviour, topology asymmetry and link failure, are major issues faced by Datacenter which result in poor performance. To handle such link failures in Datacenter network, load balancing scheme should be accurate especially path sensing and timely responses to mitigate the fallouts. Different solutions have been proposed to overcome these issues. Some of the proposed techniques are unaware about path conditions. They reroute at fixed data rate blindly. Others were capable for sensing the path condition but rerouting and adjusting the load balancing is very slow which degrade the performance. One of the good technqiue for solving the load balacing problem in Datacenter networks where multipath exits for higher data rate (parallel transmisson). That research required hardware changes, particularly for acqiuring accorate congestion feedback from end host and taking adaptiving decision for load balancing. Thus they can?t react timely to these uncertainties which results in reasonable performance degradation; especially in the worst situation to detect some issues like randomly packets drop as well as throughput of the channel. In this research, a solution has been proposed which focusses on two things (1) accurate timely acknowledgement of packet delivery, (2) Current load on each link. In our proposed work there is no need of hardware changes. We have achieved accurate response of acknowledgments of each packet delivery. This proposed scheme have been implemented using NS3 simulator. The results has been compared with the other existing solutions.