Document Details

Document Type : Thesis 
Document Title :
COMPUTATIONAL METHODS FOR THE MATHEMATICAL PHYSICS PROBLEMS
ا لطرق الحسابية لمسائل الفيزياءِ الرياضيةِ
 
Subject : mathematics department 
Document Language : Arabic 
Abstract : This thesis consists of five chapters: Chapter one of thesis is an introduction to various methods we used it and contains also the main theorems and definitions of each method. In chapter two we introduce two powerful methods to solve the Davey-Stewartson (DS) equations, one is the homotopy perturbation method (HPM) and the other is the homotopy analysis method (HAM). The sine-cosine method is used to construct periodic and solitary wave solutions. Comparsion of the HPM results with the HAM results, and compute the absolute errors between the exact solutions of the DS equations with the HPM solutions and HAM solutions. In chapter three the variational iteration method (VIM) has been applied for solving Davey-Stewartson equations and the generalized Ito system.This method is based on Lagrange multipliers for identification of optimal values of parameters in a correction functional. Using this method creates a sequence which tends to the exact solution of the problem. Comparison the absolute errors between the exact solution and VIM solution are presented. Chapter four deal with the Haar wavelet approach for numerical solution of linear integral equations is proposed. The method is applicable for different kinds of integral equations (Fredholm and Volterra equations, integrodifferential equations, weakly singular integral equations). Five test problems, for which the exact solution is known, are considered. The calculations indicate that the accuracy of the obtained solutions is quite high even when the number of calculation points is small. In chapter five we apply differential transformation method (DTM), tanh-coth method, Laplace transform method and Padé approximant for solving the equation governing the unsteady flow of a polytropic gas and the Hirota-Satsuma coupled KdV system. 
Supervisor : Dr. Hassan Ahmad Zedan 
Thesis Type : Master Thesis 
Publishing Year : 1433 AH
2012 AD 
Co-Supervisor : Dr.Wafaa Al-Barakati. 
Added Date : Sunday, December 23, 2012 

Researchers

Researcher Name (Arabic)Researcher Name (English)Researcher TypeDr GradeEmail
ندى حمد المحمديAl-Mohammadi, Nada HamadResearcherMaster 

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