A Comparison Between Some Iterative Quadrature Methods for the Numerical Solution of the Second-Kind Fredholm Integral Equations

Abstract

Some iterative Newton-cotes quadrature methods of closed and open types are presented here to solve the second-kind and linear Fredholm integral equations of both regular and singular kernels. The closed computational methods include the composite Simpson’s 1/3 quadrature, composite trapezium-corrected Simpson’s quadrature, and composite Bool’s quadrature. The errors of these quadrature formulas are analyzed and estimated. A comparison between these quadrature iterative methods is carried out by solving some second-kind Fredholm integral equations of regular kernel.  We achieve a good agreement between the exact and the numerical solutions of such equations, establishing the feasibility and applicability of the presented quadrature formulas. Furthermore, the composite Bool’s quadrature performs better than the other two quadrature formulas. The open-type Newton-cotes quadrature methods is implemented to solve the second-kind linear Fredholm integral equations of singular kernels. A comparison between the exact and the approximate solution of such equations is carried out confirming the applicability of the method