الفهرس 
Linear stationary iterative methodOnly 14 pages are availabe for public view
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Abstract
Summary
Mathematical models for most of natural laws appeared due to sci-
enti c development. As a result of human performance the mea-
sured parameters included in the mathematical methods su¤er from
the inaccuracy of the recorded measurements. As a remedy for this
inaccuracy interval and fuzzy mathematics appear in many of the
mathematical models which represent many biological and physical
phenomenons. The fuzzy parameters appeared in many mathemati-
cal models (di¤erential equations, integral equations, algebraic equa-
tions). In this thesis we focused on linear algebraic systems which
contain fuzzy parameters. Linear algebraic systems appear in the
numerical treatment of di¤erential equations and integral equations
The thesis contains four chapters, Arabic summary, English sum-
mary and a list of references.
Chapter One:
In this chapter, some basic concepts and de nitions necessary to
solve linear systems are introduced. Stationary iterative methods
such as Jacobi, Gauss Seidel, and Successive over Relaxation, KSOR
are considered. As a generalization of the previous iterative methods
the Accelerated Overrelaxation method (AOR) is presented. Some
fuzzy concepts and intervals arithmetic are studied.
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Chapter Two:
The KAOR method is introduced, which contains two relaxation
parameters. The values of the relaxation parameters at which the
method can be convergent are studied. Moreover some selected val-
ues of the relaxation parameters are considered to illustrate that
the KAOR method is a generalization of some methods like Jacobi
method and KSOR method. We also studied the convergence of the
KAOR with some types of matrices, We compared the spectral ra-
dius of the KAOR and AOR methods and showed that the selection
of the relaxation parameters in the KAOR was less sensitive around
the optimal values than in the AOR method and we illustrated this
with numerical examples.
Chapter Three:
In this chapter we studied fuzzy algebraic systems of equations
containing fuzzy coe¢ cients in the right-hand side only. We focused
on the triangular fuzzy coe¢ cients and its parametric form. The
basic idea is to convert the fuzzy system of equations into one or two
algebraic systems by using the embedding concept in two di¤erent
techniques. In the rst technique, the fuzzy system of order nn was
converted into a classical system of order 2n 2n and the solutions
were studied and displayed. In the second technique, the fuzzy system
is converted to two classic systems of type n n. We have applied
this to numerical examples.
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Summary
Chapter Four:
In this chapter, we applied the iterative methods presented in the
rst and second chapters to fuzzy systems of equations. Also, we
considered algebraic system of special construction which resulting
from the numerical treatment of boundary value problems with fuzzy
boundary conditions, results obtained are in a good value and the
subject is promising.
The thesis contains tables and gures to show and compare the
results and all calculations were implemented using the calculation
software designed using MATLAB.
It should be noted that the content of the second chapter is pub-
lished as paper entitled On the Accelerated Overrelaxation Method
in the Pure and Applied Mathematics Journal, Fourth Edition, pages
26-31, 2015. The contents of chapter four will be prepared for publi-
cation.