Blow up Method for Studying Bifurcation of Solution in Singular Perturbation Ordinary Differential Equation and Differential Algebraic Equation
| المؤلف الرئيسي: | Mnahi, Hawraa Kareem (Author) |
|---|---|
| مؤلفين آخرين: | Al-Yasiry, Kamal Hamid Yasir (Advisor) |
| التاريخ الميلادي: |
2017
|
| موقع: | الناصرية |
| الصفحات: | 1 - 72 |
| رقم MD: | 1008168 |
| نوع المحتوى: | رسائل جامعية |
| اللغة: | الإنجليزية |
| الدرجة العلمية: | رسالة ماجستير |
| الجامعة: | جامعة ذي قار |
| الكلية: | كلية التربية للعلوم الصرفة |
| الدولة: | العراق |
| قواعد المعلومات: | Dissertations |
| مواضيع: | |
| رابط المحتوى: |
عدد مرات التحميل
14
| المستخلص: |
This thesis deals with studying a new subject of a singularity perturbed ordinary differential equations system. It is considered the foundation base to get a differential algebraic equations, where the concept of singularity perturbed ODEs is explained. Then it studies the ways to deal with the perturbation parameter e through two case studies: The first case: Is the study of behavior of solution for singularity perturbed ODEs when perturbation parameter 0 <∊ ≤ 1. The above equation has been reduced by using (The implicit function theorem) for this purpose, we obtain an equation involving the central manifold and thus, applicate (Blow up method). Moreover, for this purpose of obtaining a solution curve for the system (Fast-Slow system). The second case: Is the study of behavior for perturbation parameter e when it approaches to zero. In this case we get a differential algebraic equations system that explains the relationship between the two systems. Then the bifurcation theory is applied on the last system according to singularity perturbed ODEs. In addition, sufficient conditions for the occurrence of some types of bifurcation in the solution are given, such as (Fold, Pitchfork, Trans critical and Hopf Bifurcation). Depending on the proof of theories to reduce the differential algebraic equation into ordinary differential equation using the (Implicit Function Theorem). For this purpose, proof of bifurcation that occurs in differential algebraic equation in this kind of situations is depended on the nature and behavior of the solution at the level of each state of bifurcation. |
|---|
عناصر مشابهة
-
Bifurcation of Solution in Singularly Perturbed Ordinary Differential Equations and Differential Algebraic Equations by Extended System Reduction
بواسطة: Al-Jabry, Ayat Salam Sharhan منشور: (2018) -
Advanced Multistep Methods for the Numerical Solution of Ordinary Differential Equations
بواسطة: Al Mutib, Ahmad Nassir منشور: (1994) -
Bifurcation in Differential Algebraic Equations Obtained from Singularity Perturbed ODEs and Fenichel's Theorem
بواسطة: مطر، زهراء على منشور: (2016) -
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL- ALGEBRAIC EQUATIONS USING CONTINUOUS GENETIC AIGORITHMS
بواسطة: أحمد، عمر محمد ربحي سالم السيد منشور: (2006) -
Numerical Methods for Singularly Perturbed Delay Differential Equations
بواسطة: Al Refai, Tahani Saleem Salman منشور: (2011)
