On the numerical solutions of singular initial-value problems by homotopy analysis method

Other Title(s)

الحلول العددية لمسائل القيم الإبتدائية المفردة باستخدام طريقة الفضاء التحليلي

Dissertant

al-Bashayirah, Hazem Muhsin

Thesis advisor

Mumani, Shahir

University

Mutah University

Faculty

Faculty of Science

Department

Department of Mathematics and Statistics

University Country

Jordan

Degree

Master

Degree Date

2008

English Abstract

-In this thesis, the homotopy analysis method (HAM) proposed by (Liao, 1992) is adopted to find explicit and numerical solutions for singular initialvalue problems of ordinary differential equations of second-order .

Some numerical examples and plots are presented to illustrate the efficiency and reliability of the method for singular initial-value problems.

The comparison of results obtained by the homotopy analysis method with those obtained by the homotopy-perturbation and Adomian decomposition methods reveals that the proposed method is very effective and accurate when applied to singular equations.

Also, we show that the homotopy-perturbation method is a special case of homotopy analysis method when the auxiliary parameter h = −1.

Main Subjects

Mathematics

Topics

• Mathematical analysis
• Algebra
• Differential equations

No. of Pages

33

Table of Contents

• APA
• MLA
• AMA

Language

English

Data Type

Arab Theses

Record ID

BIM-304578