الفهرس 
1 IntroductionOnly 14 pages are availabe for public view
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Abstract
Summary
The object of this thesis which consists of ve chapters, is to study
numerically by using CM and GM, the Appr. solutions, Min. error and
Max. errors for FIEs, VIEs, F-VIE and V-FIE.
At rst, in chapter one, we presented a general introduction. We focused
on basic concepts and classi cation of IEs according to their kinds and
kernels and how to convert BVBs and IVPs to IEs and vice versa. Also,
we applied Picard’s method to discuss the existence and uniqueness of
solutions for FIEs and VIEs. Finally, we presented some analytical methods
for solving IEs.
Chapter two was devoted to study the stability of error of some numerical
methods for FIEs and VIEs. We concentrated our interest on using TR,
SR, CM and GM. Also, we studied the behavior of errors at xed points
in each case, investigating the Max. and Min. errors at each point and
corresponding N of functions.
Chapter three was concerned with the behavior of the Max. and Min.
errors for F-VIE of the second kind using CM and GM. The Appr. solution
was obtained by two techniques; the 1st TM depends on representing
F-VIE as a system of FIEs of the second kind while the Appr. solution
is obtained as functions of x at xed times. In the 2nd TM, we represented
the Appr. solution as a sum of functions of x; t. Also, the
comparisons between the results which werer obtained by two techniques
in each method, were devoted. Results were represented in groups of
gures and tables.
ix
Summary x
Chapter four was focused on studying the behavior of Max. and Min.
errors of solution for V-FIE by using CM and GM.
Chapter ve was relevant to the applications of IEs in mathematical
physics and mechanics. Therefore, there are some application which
show how to convert a BVP or IVP to FIE or VIE