Document Details

Document Type : Thesis 
Document Title :
HOMOTOPY PERTURBATION METHOD AND ITS MODIFICATIONS FOR SOLVING OF NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS
طريقة الهوموتوبي الاضطرابي و تعديلاته لحل المعادلات التفاضلية العادية غير الخطية
 
Subject : Faculty of Sciences 
Document Language : Arabic 
Abstract : In this thesis, we present a new technique, namely Homotopy Perturbation Method (HPM) and some kind of its modifications to obtain the numerical solutions for nonlinear ordinary differential equations (ODEs). HPM provides a new idea for nonlinear differential equations problems. Our goals in this thesis are study the Homotopy Perturbation Method (HPM), display some efficient modifications of the HPM to obtain the numerical solutions of some problems: Riccati equation, Bratu equation, Lane-Emden equation and stiff system of ordinary differential equations which were presented as initial value problems (IVP). Several illustrative examples have been given to demonstrate the effectiveness of the present method and its modifications. Numerical comparisons between the methods HPM and the exact solution reveal that the technique is a promising, a strong and easy-to-use numerical tool for nonlinear ODEs. The obtained results show that the method is very effective and convenient in solving nonlinear ODEs. We show that the HPM is different from all numerical methods; it provides us with a simple way to adjust and control the convergence region of series solution by introducing the initial guess and auxiliary linear operator. In fact; this method often gives convergent series solution which in good agreement with the exact solution. The method approach in this thesis can be widely implemented to solve both ordinary and partial differential equations. Some of the outcome of this thesis is written in two published papers 
Supervisor : Dr. Bothayna Saleh Habiballah Kashkari 
Thesis Type : Master Thesis 
Publishing Year : 1439 AH
2018 AD 
Added Date : Wednesday, September 5, 2018 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
شريفة صالح عباسAbbas, Sharifa SalehResearcherMaster 

Files

File NameTypeDescription
 43692.pdf pdf 

Back To Researches Page