الفهرس 
Preliminary concepts
Second Degree Iterative Techniques for Integral Representation of BVPOnly 14 pages are availabe for public view
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Abstract
The thesis focuses on a numerical treatment of some differential and integral
equations starting from the standard two-point boundary value problem (BVP) of
the second order and its integral representation ending with the study of the general
fractional order BVP. The main subject of the thesis is how to reduce the given
problem to that of solving a system of algebraic equations. The thesis discusses
three techniques for this treatment: the first is the finite difference method, the
second is the Haar wavelet approach with collocation method and the third is the
shifted Chebyshev polynomials of the first kind with collocation points. Also, the
thesis considers the structure of the reduced algebraic system for the BVP and its
integral form. The rates of convergence of the iterative technique are used for the
comparison process. The thesis focuses on the three-part splitting technique for the
coefficients matrix of the algebraic system. As a final conclusion of the thesis is
using the second-degree Gauss-Siedle method for algebraic system obtained from
the integral representation is better than using the Gauss-Siedle for the
corresponding differential representation of the same problem. Also, a treatment
for a system of integral equations using Haar wavelet approach is presented. Some
numerical examples for all mentioned theoretical points were offered and the
computational results were consistent with the theoretical studies.
Key words: Boundary value problems, Fredholm Integral equations, Finite
difference method, Haar wavelet, Chebyshev Polynomials, Iterative techniques.