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The Numerical Solution of Integral and Integro-Di Erential Equations by Wavelet Collocation Method

Thesis Info

Access Option

External Link

Author

Khan, Imran.

Program

PhD

Institute

University of Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2018-04

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/9326/1/Imran_Khan_Maths_HSR_2018_UoP_Peshawar_13.09.2018.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727586892

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This thesis presents some new algorithms for the numerical solution of IEs, IDEs and PIDEs. These new algorithms are based on WCM. The focus is upon two types of wavelets namely HW and LLMWs both having compact support. HW has already been applied for numerical solution of IEs and IDEs by a few re- searchers and the numerical results can be found in the existing literature. One draw back of the HWCM is its slow convergence. In order to improve the convergence rate we have applied LLMWCM to IEs and IDEs. In most of the cases of the IEs and IDEs we obtained better results with LLMWCM as compare to HWCM. We also extended the existing HWCM for IEs and IDEs in the literature as well as the newly developed LLMWCM for IEs and IDEs in this thesis to numerical solution of some particular type of PIDEs. Both the HWCM and LLMWCM are thoroughly investigated in this thesis for numer- ical solution of di erent types of IEs, IDEs and PIDEs including Fredholm, Volterra and Fredholm-Volterra IEs, IDEs and PIDEs. The methods are also investigated for higher- order IDEs. An important characteristics of the method is that it can be applied to both linear and nonlinear problems. In the present work, in case of solving linear IEs, IDEs and PIDEs, the resulting systems will be solved by using Gauss elimination method, while for nonlinear case, we use Newton''s or Broyden''s method. All methods are implementing and testing by a computer programming software MATLAB. Several test problems are performed in order to verify the accuracy and e ciency of the present methods. The experimental rates of convergence and MAEs have been calculated for di erent number of CPs. The approximate solution of these test problems are compared with exact solutions and also the numerical results are compared with other well established methods to show better e ciency, accuracy and simple applicability of the newly developed methods. A comparative study of HWCM and LLMWCM is also perform in this thesis.
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مولانا سید اصغر حسین

مولانا سیداصغر حسین
صد حیف کہ آسمانِ علم و عمل اور فلکِ شریعت وطریقت کاایک اورکوکبِ درخشندہ ٹوٹ گیا یعنی حضرت مولانا سیداصغر حسین صاحبؒ المعروف بہ میاں صاحب نے ۸؍ جنوری۴۵ء کوبمقام راندیر ضلع سورت انتقال فرمایا۔انا ﷲ وانا الیہ راجعون۔
حضرت میاں صاحب ؒ ان بزرگوں میں سے تھے جن کو بے تامل مادر زاد ولی کہا جاسکتا ہے۔ علوم ظاہر وباطن دونوں کے جامع تھے۔ دارالعلوم دیوبند میں تعلیم پائی، آپ کاشمار حضرت شیخ الہند ؒکے ارشد تلامذہ میں تھا۔دارالعلوم دیوبند سے فارغ التحصیل ہونے کے بعد مختلف مقامات میں بسلسلۂ تعلیم وتدریس مقیم رہے۔ان مقامات میں جونپور کواس لحاظ سے خاص امتیاز حاصل ہے کہ حضرت مرحوم کاقیام وہاں قدرے ممتدرہا اور وہاں کے مسلمانوں نے آپ کے وجود سے بہت کچھ فیضِ ظاہری و باطنی حاصل کیا۔
اب سالہاسال سے دارالعلوم دیوبند میں حدیث کے استاذ اعلیٰ تھے۔تفسیر کی بھی بعض اونچی کتابیں (تفسیر ابن کثیر وغیرہ) آپ کے درس میں رہتی تھیں، حدیث کی مشکل ترین کتاب سننِ ابوداؤد ہمیشہ آپ ہی کے یہاں رہتی تھی اورحق یہ ہے اس اہم کتاب کی عقدہ کشائی آپ جس فنی حذاقت سے فرمایا کرتے تھے وہ آپ ہی کاحصہ تھا۔حدیث کے علاوہ فقہ میں خصوصاًاوردوسرے علوم دینیہ و الٰہیہ میں استعداد پختہ اورنظر وسیع رکھتے تھے۔ درس میں بولتے کم تھے مگر جوبات فرماتے تھے نہایت جچی تلی اورٹھوس ہوتی تھی۔حضرت الاستاذ علامہ سیدمحمد انورشاہ صاحبؒ اپنے حلقۂ درس میں آپ کی ذہانت وفطانت کی داد دیا کرتے تھے۔ فرمایا کرتے تھے میاں صاحب’’فقیہ النفس ‘‘ہیں ۔علاوہ بریں آپ اردو زبان میں تصنیف وتالیف کاشگفتہ اور سلجھا ہوامذاق بھی رکھتے تھے۔’القاسم‘ اور’الرشید‘ کے دورِ قدیم میں دونوں میں علمی ودینی مباحث پرمضامین لکھتے تھے۔ان کے علاوہ چھوٹی بڑی متعدد کتابیں اور مستقل رسالے بھی تصنیف کیے ہیں جو چھپ کرملک میں شائع اور...

The Extent to Which Pupils Have Adopted the Values of Middle School English Book Year Three

The present study aims at determining the extent to which the values, derived from the second-generation curriculum and introduced in the third-year middle school English book, are adopted by teenagers to help them overcome their identity crisis, in Algeria. To achieve this aim, two questionnaires applied to 70 third year teenage pupils were carried out. One prior to the study with the third year English book, the other one after the study.The results of the two questionnaires were compared and showed that the values total average has increased from 16.06 in the first questionnaire to 21.33 in the second. An increase has also been noticed in the averages of the four value dimensions: national identity (from 4.76 to 6.10), national awareness (from 3.63 to 5.36), citizenship (from 4.13 to 5.31) and openness to the world (from 3.50 to 4.50). The previous results confirm that there is an improvement in the values of pupils yet the commitment to the values of « openness to the world » dimension is still weak compared to the other ones and needs further research to be improved.

Investing Job Satisfaction of Teachers in Karachi, Pakistan: A Survey Study

Job satisfaction is an important but a very complex issue, as it is all about human behavior, which is difficult to measure (Saiti, 2007). Knowledge of an employees' level of satisfaction is important for both the organization and the employee because of its (job satisfaction) association with workplace productivity. Furthermore, the knowledge of employees' lack of satisfaction with certain facets of the job will also prompt necessary measures by the employer for improving that aspect, so that the employees' well-being and productivity can be improved. The studies around the area of job satisfaction have explored various aspects of a job and the relationship between job satisfaction and the contributing factors affecting it, which, sometimes, have yielded inconsistent and contradictory findings. The present study is an attempt to explore job satisfaction of teachers of private and government schools in the context of Pakistan. In particular, the study aimed at exploring the overall level of job satisfaction of teachers of Karachi, Pakistan and to see if there is a difference of satisfaction with job between government and private schools' teachers. An important focus of the study was to see to what extent demographic characteristics such as, age, qualification, length of service and salary affect teachers' satisfaction level. A questionnaire of Job Satisfaction Survey (Spector, 1985) was adapted and administered on 500 private and government teachers with a return rate of 69%. SPSS was used to analyze the data generated from the survey. The findings of the analysis revealed that the teachers were somewhat satisfied with their overall job. A comparison between private and government teachers showed that the private school teachers had a higher level of satisfaction with their job than their government counterparts. The analysis also revealed varied level of relationship between demographic characteristics and job satisfaction. The findings show that the level of job satisfaction decreases as the teachers' length of service increases. In a similar way, satisfaction with job also decreases as teachers' age increases. Salary was also found to have negative correlation with job satisfaction, which means the more the salary, the lesser the teachers' job satisfaction, whereas academic and professional qualifications were not found to have any association with job satisfaction