Search or add a thesis

Advanced Search (Beta)
Home > Haar Wavelet Approach for Numerical Solution of Ordinary, Partial and Fractional Differential Equations With Delay

Haar Wavelet Approach for Numerical Solution of Ordinary, Partial and Fractional Differential Equations With Delay

Thesis Info

Access Option

External Link

Author

Rohul Amin

Program

PhD

Institute

University of Peshawar

City

Peshawar

Province

KPK

Country

Pakistan

Thesis Completing Year

2017

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/8184/1/Rohul_Amin_Maths_2017_HSR_UoP_Peshawar_22.06.2017.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676726353996

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


In this thesis, the main emphasis is on collocation technique using Haar wavelet. A new method based on Haar wavelet collocation is being formu- lated for numerical solution of delay differential equations, delay differential systems, delay partial differential equations and fractional delay differential equations. The numerical method is applied to both linear and nonlinear time invariant delay differential equations, time-varying delay differential equa- tions and system of these equations. For delay partial differential equations two methods are considered: the first one is a hybrid method of finite differ- ence scheme and one-dimensional Haar wavelet collocation method while in the second method two-dimensional Haar wavelet collocation method is ap- plied, and a comparative study is performed between the two methods. We also extend the method developed for delay differential equations to solve nu- merically fractional delay differential equations using Caputo derivatives and Haar wavelet. Here we consider fractional derivatives in the Caputo sense. Also we designed algorithms for all the new developed methods. The imple- mentations and testing of all methods are performed in MATLAB software. Several numerical experiments are conducted to verify the accuracy, ef- ficiency and convergence of the proposed method. The proposed method is also compared with some of the existing numerical methods in the literature and is applied to a number of benchmark test problems. The numerical re- sults are also compared with the exact solutions and the performance of the method is demonstrated by calculating the maximum absolute errors, mean square root errors and experimental rates of convergence for different number of collocation points. The numerical results show that the method is simply applicable, accurate, efficient and robust
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

آیاتِ استفہام اور فہم عقیدہ آخرت

کائنات کے نظام کا مطالعہ کرنے سے پتہ چلتا ہے کہ یہاں کسی چیز کے لئے کبھی ہمیشگی نہیں ہے، سب کی ایک عمر مقرر ہے وہ اپنی عمر مکمل کرنے کے بعد ختم ہوجاتی ہے، اس کائنات کو کمال درجہ حکمت سے بنایا گیا ہے جس کی ہر شئے میں ایک قانون کار فرما ہے۔ دنیا میں نیکی و بدی، ظلم و عدل اور تعمیر و تحریک کرنے کے بعد مٹی میں مل جانا یہ حقیت نہیں ہے بلکہ ہر اچھائی اور برائی کا بدلہ ضرور ملے گا۔

حافظ عمران ایوب لاہوری اپنی کتاب ’’آخرت کی کتاب‘‘ میں لکھتے ہیں کہ:

 "آخرت ان تمام امور کا نام ہے جو مرنے کے بعد انسان کو پیش آئیں گے آخرت کے لیے کہا گیا ہے کہ یہ دنیا کے بعد آنے والی ہے آخرت پر ایمان پر قائم ان میں سے ایک اہم رکن ہے کہ جب تک آخرت کے متعلق اللہ تعالی کی بتلائی ہوئی ہر خبر پر دل ایسا مطمئن نہ ہو جائے کہ کسی قسم کا شک و شبہ باقی نہ رہے تب تک ایمان بالآخرت کا حصول ممکن نہیں اور ایسا اعتقاد رکھنے والا ہی حقیقی مومن ہے اس کے علاوہ آخرت پر ایمان کا یہ فائدہ ہے کہ اس سے رغبت، خوف اور اعمال صالحہ کی بجاآوری کے ذریعے رب العالمین کی خوشنودی حاصل کرنے کا جذبہ پیدا ہوتا ہے ہر جاندار نے موت کا ذائقہ چکھنا ہے اور جو بھی ذی روح اس دنیا میں آیا ہے اس نے بالآخر یہاں سے رخصت ہونا ہے کوئی بھی موت سے نہیں بچ سکتا چاہے وہ خود کو مضبوط قلعوں میں بند ہی کیوں نہ کرلے اس لئے موت کو ہمیشہ یاد رکھنا چاہیے نبی صلی اللہ علیہ وسلم نے نصیحت فرمائی ہے کہ موت کو کثرت سے...

غربت کے خاتمہ کے لیے ازواجِ مطہرات کی مساعی

Islam as a religion is not based on empty or futile theories. Infact it intensely educates in altering a practical approach towards ones exixtence both as an individual and or a social being. It is the only religion which lead the way towards welfare/ "Falah" and Qura Calls such people Muflihon. Falah is for both render, either it is a man or a woman. Women especially Holy Prophet's wives are never leave behind in poor's uplift and public welfare. From the very beginning of UMMAHATUL-MOMINEEN (Holy Prophet's wives) are playing vital role in social or public welfare an till in this modern era and patriarchal society, they are role model to help plebians. The Islamic values as the world knows of them today were brought to light through our last messanger (P.B.U.H), assigned with the most important task in probably the most crucial era of human history. With the injustice all over the globe and the leaders of super powers in a rift with each other to dominate the world, exhausted the most important of resouces i.e. The humanity. The divine manifiesto of the Prophet Muhammad (P.B.U.H) and the lives of wives of Holy Prophet was actually based upon justice among masses and the preservation of conflict torn humanity. The intellectual wisdom of Holy Prophet's wives in the given situation was to restore order while restoring justice based upon the reformative rule of law as depicted by the Islamic ideology. The main aim of this very importatnt initiative was to reintroduce the humanity with the most important elements such as humility, mutual respect an retoration of long forgotten code of ethics. The basic foundation of our last Prophet's wives idealogy was to uplift poor whether they are Muslims or not. They successfully ordained the resurfacing, prevalence and practice of the same code of ethics. Now days many of such examples are prevalent in the world, not as a whole yet, though to a certain extent which is holding it together. The war torn and devastated west of the medieval found its solution in applying the same Islamic rule of law in their society in late 17th century and onward. It therefore can be deduced that the same code of ethics, which can be referred to the Quran, the sacred Islamic book, possibly offers the most effective solutions in order to ensure the societal and social development in current era.

The Deoband Movement and the Rise of Religious Militancy in Pakistan.

Research studies investigating the rise of religious violence in Pakistan invariably identify Deobandis as the most violent of all religious groups in Pakistan. These studies outline a number of factors regarded important for understanding the upsurge of religious militancy in Pakistan but fails to give any explanation that why these factors led to the militarization of the Deobandis and no other religious group. The present study is an attempt to fill this gap in the available literature. The scholarly studies that attempt to explain and analyze the unprecedented upsurge of religious militancy in Pakistan have identified a number of exogenous and endogenous factors as the root causes of the said militant activism. The endogenous factors given in these studies are; Pakistan’s ideological foundations, Zia’s Islamization program and certain socio-economic changes brought about by remittances from the Gulf countries. While the exogenous factors include; Shia activism in Pakistan in the wake of the Iranian Revolution of 1979 and the pouring in of funds from some of the Gulf States to curtail the same, Pakistan’s military’s Kashmir policy, Soviet intervention in Afghanistan and Zia’s military regime’s decision to support Afghan resistance to it, with help from U.S., Saudi Arab and Egypt. These endogenous and exogenous factors which have been termed in the present study as the enabling factors of militancy do not explain their unequal effect on different religious groups. It is the contention of the present study that the increasing resort of the Deobandis to militancy for the fulfillment their political objectives is the outcome of their religiopolitical approach. The study shows that it is the particular religio-political orientation of the Deobandis that works as a motivation for using violence and are accordingly called the motivational factors of militancy. The thesis argues that the Deobandi inclination to use violence could be explained only by taking into account these motivational factors For a better theoretical understanding of the Deobandis resort to violence the study proposes a synthesis of the primordialist and circumstantialist approaches. It is the contention of this study that the use of either the primordialist or circumstantialist approach fail to effectively explain the Deobandi inclination to use violent means for their objectives more than any other religious group in Pakistan. For probing the religio-political orientation of the Deobandis a thorough study of the writings of the leading Deobandi ulama has been undertaken. The knowledge obtained from this enormous body of literature is augmented by interviews and discussions with relevant people and at times by participant observation. It is on the basis of the knowledge thus derived that the thesis disagrees with the view that the Deoband was ever an apolitical, quietist and inward-looking pietistic movement. In this regard even the claims of the Tablighi Jamaat to complete political aloofness are found to be not entirely correct. The study gives a detailed account of the political activities of the Deobandis since the time of their ideological predecessors and shows that the ulama had never shun politics and propose that the outward political quietism was projected only for diverting the attention of the state under the British. It is further argued that the denial of any political or militant activity under inopportune circumstances and owning it when the circumstances are opportune is an important facet of the religio-political approach of the Deobandis. The study also affords an analysis of the religious orientation of the Deobandis and contends that the self-proclaimed responsibility of the Deobandis, with regard to policing the boundaries of the faith, is the outcome of their distinct religious approach. By restricting the study of rational sciences and turning madrassah from an informal space for the dissemination of a variety of Islamic learning into institutions of a restricted sectarian education aiming only at the production of self-conscious pious bodies made the products of the Deobandi madrassahs bigots inclined to use violence against the religious other. It is because of this religio-political orientation that the Deobandis not only played leading role in the sectarian violence in Pakistan but also willingly fought the proxy jihad in Afghanistan and Kashmir at the behest of the Pakistani state. In the final analysis the thesis argues that the enabling factors of militancy outlined in the foregoing only explains the timing, magnitude and sustenance of the religious violence but its occurrence in the first place would not have been possible without the strong motivation on the part of the Deobandis to use violence for the fulfillment of their self-proclaimed responsibility for the upholding of Islam, as they interpret and define it. But as the enormous scale on which the religious militancy is presently occurring is because of the enabling role of the state the study proposes that its level and effect could be minimized if the state stops flirting with Islam for short term political gains. It is further proposed that the state undertakes serious, long-term and meaningful efforts for building a narrative to counter the narrative that sanctions a resort to violence.