Approximate Solution of Linear Fredholm Integral Equation of the Second Kind Using Modified Simpson's Rule

Abstract

In this paper, we introduce a novel approach to obtain approximate numerical solutions of linear Fredholm integral equations of the second kind. This method is founded on the modified Simpson's quadrature rule. We transform the Fredholm integral equation of the second kind into a system of linear equations and provide numerical examples. Numerical results were compared and interpreted with tables and graphs and the solution was shown to be consistent. Furthermore, we conduct a comparative analysis, comparing the absolute error in the solution with existed methods This comparison serves to highlight the efficiency and accuracy of our proposed method.