Numerical solution of linear Fredholm integral equations via modified Simpson’s quadrature rule

Abstract

The main purpose of this paper is to demonstrate that using modified Simpson's quadrature rule for solving linear Fredholm integral equations of the second kind. We convert the integral equations to a system of linear equations, and by using numerical examples we show our estimation have a good degree of accuracy.

Study of Nonlocal Boundary Value Problem for the Fredholm–Volterra Integro-Differential Equation

“…ere are also many authors interested in studying the numerical solution for integral and integrodifferential equations. Mirzaee and Piroozfar used modified Simpson's quadrature rule for solving linear Fredholm integral equations of the second kind [5]. Rahman et al solved the system of linear Volterra Integral equations of the second kind using Simpson's quadrature rule [6].…”

“…Existence of SolutionDefinition 1. By a solution of Fredholm-Volterra integral equation(9), we mean a functionu(x) ∈ C[a, b]that satisfies(5). Let the assumptions (1)-(5) hold.en, Fredholm-Volterra integral equation (9) has at least one solutionu(x) ∈ C[a, b].…”

Modified Midpoint Method for Solving System of Linear Fredholm Integral Equations of the Second Kind

“…The uses of modified quadrature formula for solving integral equations and their systems have been considered by many authors: modified trapezoidal [11][12][13], modified Simpson's [13][14][15][16] and modified midpoint method [17].…”

Half-Sweep Geometric Mean Iterative Method for the Repeated Simpson Solution of Second Kind Linear Fredholm Integral Equations

“…To solve Eq. (1.1) numerically, we either seek to determine an approximate solution by using the quadrature method [8,11,12,14,15,20], or use the projection method [5,6,9,10]. Such discretizations of integral equations lead to dense linear systems and can be prohibitively expensive to solve using direct methods as the order of the linear system increases.…”