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Variational Iteration Technique and Numerical Methods for Solving Nonlinear Equations

Thesis Info

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Author

Shah, Farooq Ahmed

Program

PhD

Institute

COMSATS University Islamabad

City

Islamabad

Province

Islamabad.

Country

Pakistan

Thesis Completing Year

2012

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/handle/123456789/1737

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727657741

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Various problems of pure and applied sciences such as physics, chemistry, biology, engineering, economics, management sciences, industrial research and optimization can be studied in the unified frame work nonlinear equation f ( x) = 0. In this thesis, we use the variational iteration technique and its various modifications to suggest and analyze several iterative methods for finding the approximate solution of the nonlinear equations. Using suitable finite difference schemes, a number of new iterative methods free from second derivative are considered and analyzed. Variational iteration technique is also used to find the multiple roots of nonlinear equations with known and unknown multiplicity. Several examples are given to illustrate the efficiency and implementation of these new methods. Comparison with other methods is given to show the performance of new methods.
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نواب صلابت بہادر

نواب صلابت بہادر
یہ خبر نہایت حسرت و افسوس کے ساتھ سنی جائے گی کہ اعلیٰ حضرت خسرو دکن خلداﷲ ملکہ کے چھوٹے بھائی نواب صلابت خان بہادر نے ستائیس سال کی عمر میں چند روز بیمار رہ کر رحلت فرمائی، مرحوم شاہی خانوادہ آصفی کے ایک رکن رکین ہونے کے علاوہ مشرقی علوم و ادب سے پوری دلچسپی رکھتے تھے، اﷲ تعالیٰ مرحوم نوجوان شہزادہ کے سر پر اپنے الطاف و رحمت کاتاج رکھے اور اعلیٰ حضرت برادر اکبر اور دیگر اعزہ کو صبر و سکون اور رضا بالقضا کی غیرفانی دولت سے ممتاز فرمائے۔ (سید سلیمان ندوی، مارچ ۱۹۳۴ء)

 

مالكانہ تصرفات پر نفاذ حجر كے اسباب

Where Islam takes the protection of human life on first priority there it places the fluctuation and safety of one's property and ownership on the second priority_ Qura’nic Verses, sayings of the Prophet and civil and criminal juristic laws stress the protection of property__ The extravagancy, misuse, theft, robbery, usurpation, aleatory, deception and alike have been termed unfair means regarding the property. Besides, according to Muslim jurists there are some other elements, if not checked may lead to deterioration of property_ like disposition of property during immaturity, lunacy, drunkenness and inebriety, stupidity etc. In this connection Islamic Law introduces the rules of Hajr (interdiction) which ensure the sanction upon such a person found suffering from the above imperfection and forbids him to make disposition in his own property and terms it invalid for further legal effects. In juristic terminology such rules are called Hap (interdiction) .

Comparison of Outcomes of Open Reduction Versus Open Reduction Salter Osteotomy for Developmental Dysplasia of the Hip Ddh Among Children at French Medical Institute for Children, Kabul, Afghanistan

Background: Developmental Dysplasia of the Hip (DDH) consists of either subluxation or dislocation of femoral head from acetabulum and acetabular dysplasia. The ratio of left side hip to right is 3:1. There are several kinds of treatments for DDH globally, and conservative treatment is one of the best methods with a better outcome than surgical treatment. Objective: The aim of this research study is to compare the outcomes of Open Reduction versus Open Reduction Salter Osteotomy with regard to length of stay, complications and family satisfaction among children with DDH at FMIC, Kabul, Afghanistan. Methodology: A retrospective cohort study design was employed. Records of 166 participants who underwent Open Reduction and Open reduction Salter Osteotomy at FMIC hospital were reviewed. The data was collected from the available records during the period of 2010 to 2015. Chi-square test of independence and T-test for two independent samples were run to determine an association between two categorical variables and compute mean difference between categorical and continuous variables for two types of surgical procedure for DDH respectively. In addition, t-test for two dependent samples was also run to compare the mean difference of Pre-operation and Post-operation AI. All the ethical principles were followed throughout the study process. Result: The research findings revealed that there is a difference in outcomes of Open Reduction versus Open Reduction Salter Osteotomy. There was a meaningful difference of Pre-operation and Post-Operation AI for DDH patients (p-value <0.001). Hospital length of stay for Open Reduction group was relatively low (p-value <0.001). The rate of development of complications was higher in Open reduction group as compared to Open reduction Salter osteotomy. Residual dysplasia is more common in open reduction group, 16 participants (19.27%) as compared to open reduction salter osteotomy 9 (10. 84%). In open reduction group only 1 (0.6%) of the participants had subluxation, and 2 (1.2%) others developed femoral head AVN. On the contrary, in the open reduction salter osteotomy group, 1 (0.6%) participant had developed subluxation and 5 (3%) had developed AVN and majority of participants 132(79.5%) had not developed any complications. Half of participants’ families 101 (60.8%) were strongly satisfied, followed by 62 (37.3%) satisfied, and while 3 (1.8%) were dissatisfied with two types of surgical treatment methods. 132 (79.5%) of participants had excellent outcome, 25 (15.1%) good, 2(1.2%) and 7 (4.2%) poor outcome. Conclusion: The research study revealed that there is difference in the outcomes of