Abstract: The objective of this paper is to analyse the
application of the Half-Sweep Gauss-Seidel (HSGS) method by using
the Half-sweep approximation equation based on central difference
(CD) and repeated trapezoidal (RT) formulas to solve linear fredholm
integro-differential equations of first order. The formulation and
implementation of the Full-Sweep Gauss-Seidel (FSGS) and Half-
Sweep Gauss-Seidel (HSGS) methods are also presented. The HSGS
method has been shown to rapid compared to the FSGS methods.
Some numerical tests were illustrated to show that the HSGS method
is superior to the FSGS method.