Some applications of the variational iteration method in solving differential equations
Other Title(s)
تطبيقات لطريقة التكرار المتغاير في حل معادلات تفاضلية
Dissertant
Thesis advisor
Comitee Members
al-Butush, Ratib Hamid
Masadah, Basem
Udaybat, Zayd Muhammad
University
Mutah University
Faculty
Faculty of Science
Department
Department of Mathematics and Statistics
University Country
Jordan
Degree
Master
Degree Date
2005
Arabic Abstract
في هذه الأطروحة، سنتناول طريقة جديدة تدعى (طريقة التكرار المتغاير) لحل نوعين من المعادلات التفاضلية : 1) معادلة تفاضلية عادية محدودة غير خطية.
2) معادلات تفاضلية جزئية : معادلة فيشر، معادلة فيشر العامة، معادلة الانتشار غير الخطية من نوع فيش، معادلة تفاضلية لقطع مكافئ محدودة و بشروط أولية.
لتوضيح هذه الطريقة تم وضع العديد من الأمثلة، كذلك تم مقارنة النتائج مع إحدى الطرق المهمة في حل المعادلات التفاضلية تسمى (طريقة تجزئة ادومين).
المقارنة بين الطريقتين تبين أن (طريقة التكرار المتغاير) هي طريقة فعالة و تعالج المشكلات التي يمكن الحصول عليها بالطرق الأخرى.
English Abstract
In this thesis, we implement a new analytical technique, the He's variational iteration method for solving two types of differential equations.' 1) A nonlinear ordinary boundary value problem 2) Partial differential equation : (Fisher's equation, the general Fisher's equation, a nonlinear diffusion equation of the Fisher type, parabolic partial differential equation with boundary and initial conditions).
The numerical and analytical solutions of the above equations have been obtained in terms of a convergent power series with easily computable components.
Numerical examples are given and comparisons are made with the Adomian decomposition method, the comparison shows that the variational iteration method is more effective and overcome the difficulty arising in calculating Adomian polynomials.
Main Subjects
Topics
No. of Pages
55
Table of Contents
Table of contents.
Abstract.
Chapter one : introduction.
Chapter two : the variartional iteration method.
Chapter three : variational iteration method for solving boundary value problems.
Chapter four : variational iteration method for solving fisher's equation.
Chapter five : conclusions and summary.
References.
American Psychological Association (APA)
Abu-Assad, Salah Abd al-Latif. (2005). Some applications of the variational iteration method in solving differential equations. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-309612
Modern Language Association (MLA)
Abu-Assad, Salah Abd al-Latif. Some applications of the variational iteration method in solving differential equations. (Master's theses Theses and Dissertations Master). Mutah University. (2005).
https://search.emarefa.net/detail/BIM-309612
American Medical Association (AMA)
Abu-Assad, Salah Abd al-Latif. (2005). Some applications of the variational iteration method in solving differential equations. (Master's theses Theses and Dissertations Master). Mutah University, Jordan
https://search.emarefa.net/detail/BIM-309612
Language
English
Data Type
Arab Theses
Record ID
BIM-309612
