A refinement sum-technique in an iterative scheme adapted for a linear system of integral equations to approach a Fredholm integral equation's solution

Based on the use of the geometric series theorem, we transform a linear Fredholm integral equation of the second kind defined on a large interval into an equivalent linear system of Fredholm integral equations of the second kind; then, we inflict a refinement in the way the investigated generalised iterative scheme approximates the sought-after solution. By avoiding to inverse a bounded linear operator, and computing a truncated geometric sum of the former's associated sequence of bounded linear operators instead, we notice that our approach furnishes a better performance in terms of computational time and error efficiency.