Numerical solutions of second kind Fredholm integral equations using Half-Sweep Geometric Mean method

In this paper, numerical solution of the dense linear systems that arise from the linear second kind Fredholm integral equation was studied. The half-sweep geometric mean (HSGM) iterative method is applied to solve linear systems generated from discretization of the linear Fredholm integral equations of the second kind using repeated trapezoidal (RT) and modified repeated trapezoidal (RMT) schemes. In addition, the formulation and implementation of the full-sweep geometric mean (FSGM) and HSGM methods are also presented. Some illustrative examples are given to demonstrate the efficiency of the proposed method.