Search or add a thesis

Advanced Search (Beta)
Home > Some Wavelet Schemes for Nonlinear Differential Equations

Some Wavelet Schemes for Nonlinear Differential Equations

Thesis Info

Access Option

External Link

Author

Iqbal, Muhammad Asad

Program

PhD

Institute

HITEC University

City

Taxila

Province

Punjab

Country

Pakistan

Thesis Completing Year

2015

Thesis Completion Status

Completed

Subject

Mathemaics

Language

English

Link

http://prr.hec.gov.pk/jspui/bitstream/123456789/2786/1/Muhammad_Asad_Iqbal_Maths_2016_HSR_HITEC_10.11.2016.pdf

Added

2021-02-17 19:49:13

Modified

2024-03-24 20:25:49

ARI ID

1676727211115

Asian Research Index Whatsapp Chanel
Asian Research Index Whatsapp Chanel

Join our Whatsapp Channel to get regular updates.

Similar


This work is devoted to the study of wavelet schemes for solving nonlinear differential equations. Most of the scientific and engineering phenomena can be represented in the form of nonlinear differential equations. Over the past few decades, nonlinear differential equations have been the core of research for many researchers and scientists. Owing to the non-availability of exact solutions in many nonlinear physical problems representing complex phenomena, various analytical and non-analytical schemes have been evolved. One of the most recent families of schemes developed for finding solutions of differential equations is Wavelet schemes. These newly revolutionized schemes have few shortcomings, while dealing with nonlinear differential equations. The existing wavelets schemes are being modified and enhanced in this study to overcome these shortcomings. In this study, techniques such as Picard’s Iteration Method, Quasilinearization Method and Method of Steps have been merged with different wavelet schemes, which proved to be very proficient, reliable and effective in handling a large number of nonlinear mathematical problems representing nonlinear differential equations and their systems. These wavelet schemes have been extended for fractional nonlinear differential equations also.
Loading...
Loading...

Similar Books

Loading...

Similar Chapters

Loading...

Similar News

Loading...

Similar Articles

Loading...

Similar Article Headings

Loading...

اسم ِ استفہامیہ : کم؟(کتنا)

اسم ِ استفہامیہ :کم؟(کتنا)

ارشارِ ربانی ہے:

"كَمْ أَهْلَكْنَا مِنْ قَبْلِهِمْ مِنْ قَرْنٍ فَنَادَوْا وَلَاتَ حِينَ مَنَاصٍ"۔ [[1]]

" کتنی ہی امتوں کو ہم (عذاب سے) ہلاک کر چکے ہیں سو انہوں نے (ہلاکت کے وقت) بڑی ہائے پکار کی اور وہ وقت خلاصی کا نہ تھا"۔

یعنی ان کو معلوم رہنا چاہیے کہ اسی غرور وتکبر کی بدولت انبیاء اللہ سے مقابلہ ٹھان کر بہت سی جماعتیں پہلے تباہ و برباد ہو چکی ہیں وہ لوگ بھی مدتوں پیغمبروں سے لڑتے رہے۔ پھر جب برا وقت آ پڑا اور عذاب الٰہی نے چاروں طرف سے گھیر لیا تو گھبرا کر شور مچانے اور خدا کو پکارنے لگے۔ مگر اس وقت فریاد کرنے سے کیا بنتا۔ خلاصی کا موقع گزر چکا تھا، اور وقت نہیں رہا تھا کہ ان کے شوروبکاء کی طرف توجہ کی جائے۔



[[1]]         القرآن ، ۳۲: ۲۸۔

پاکستان میں رائج زرعی نظام کا شرعی جائزہ

Islam has provided guidance in agriculture like any other field of life. Agriculture provides food and nourishment to men, animals and birds. Pakistan is an agricultural land. Out of total grass root of Pakistan economy, 80% depends upon the agriculture. Agriculture is the production of food, feed and fiber by the systematic harvesting of plants and animals. The history of agriculture is a central element of human history. The article deals with the study of Muslims’ contribution to agriculture especially the Prophetic and four caliphs’ time. The Prophet r initiated the development of a sophisticated system of irrigation, and the Caliphs Hazrat Umar R. A and Hazrat Uthman R. A suggested revolution in agricultural reforms. The Islamic rules on land ownership and labor rights, alongside the recognition of private ownership and introduction of share cropping created by incentives to engage in agriculture. The present system prevailing in Pakistan has several short comings. Landlordism and poverty of cultivators who are generally uneducated, absence of heavy machinery for cultivation and small holdings also create problem.

Production and Characterization of Pectinases by Aspergillus Niger for Industrial Use

Two hundred and sixteen fungal strains were isolated from two hundred fifty soil samples collected from different localities of Punjab and subjected to screening for their pectinolytic ability using submerged fermentation. One hundred and fifty one pectinolytic strains were subjected to secondary screening and isolate IIB-13 gave the maximum pectinase yield (10.78±0.45U/ml/min) and identified as Aspergillus niger using morphological characteristics. Random mutagenesis (physical and chemical) was used to improve the pectinolytic activity of strain IIB-13. Nitrous acid mutant H-97 resulted in three fold increase (32.16 + 0.05U/ml/min) in pectinase production. This H-97strain was further subjected to optimization of media, carbon and nitrogen sources, temperature and pH. Maximum pectinase (37.01±0.11 U/ml/min) was produced using medium containing K2HPO4 (4.0 g), yeast extract (0.6 g), KH2PO4 (1.28 g), (NH4)2SO4 (2.0 g), MgSO4 (1.1 g) and pectin (10 g) per 1.0 L of distilled water at pH and temperature (7.0 and 30°C) respectively after 60 hours of fermentation. Fermenter studies (7.5 L) resulted in increased pectinase activity (40.31±0.07 U/ml/min) with decreased incubation time of 48 h using 1% inoculums with optimized reaction conditions i.e. temperature (30°C), pH (07), agitation (200 rpm) and aeration (1vvm). Fermentation kinetics was applied to validate the results. The crude enzyme was subjected to purification by applying ammonium sulfate precipitation and Ion exchange chromatography which resulted in 44.20 % yield with increased activity i.e. 75.18±0.04 U/mg. Km value of 2.30 mg/ml using pectin as substrate showed its maximum specificity for the enzyme. Activation energy (Ea) i.e. -28.95 KJ/mol and enthalpy of activation (ΔH) i.e. -26.73 KJ/mol were calculated employing thermodynamic studies. Characterization of enzyme revealed catalytic activity optimum temperature and pH as 25°C and pH 7. The enzymes catalytic activity was observed to be reduced by some heavy metals such as Hg2+, Pb2+, Cu+ and Cd2+.