scholarly journals Nyström methods for Fredholm integral equations using equispaced points

Filomat ◽  
2014 ◽  
Vol 28 (1) ◽  
pp. 49-63 ◽  
Author(s):  
Donatella Occorsio ◽  
Maria Russo
Keyword(s):  
Integral Equations ◽  
Order Of Convergence ◽  
Quadrature Rule ◽  
Fredholm Integral Equations ◽  
Numerical Tests ◽  
Nyström Methods

In this paper we investigate some Nystr?m methods for Fredholm integral equations in the interval [0, 1]. We give an overview of the order of convergence, which depends on the smoothness of the involved functions. In particular, we consider the Nystr?m methods based on the so called Generalized Bernstein quadrature rule, on a Romberg scheme and on the so-called IMT rule. We prove that the proposed methods are convergent, stable and well conditioned. Also, we give several numerical tests for comparing these three methods.

scholarly journals Solution of second kind Fredholm integral equations by means of Gauss and anti-Gauss quadrature rules

2020 ◽  
Vol 146 (4) ◽  
pp. 699-728
Author(s):  
Patricia Díaz de Alba ◽  
Luisa Fermo ◽  
Giuseppe Rodriguez
Keyword(s):  
Integral Equations ◽  
Numerical Approximation ◽  
Gauss Quadrature ◽  
Upper And Lower Bounds ◽  
Stability And Convergence ◽  
Quadrature Rules ◽  
Fredholm Integral Equations ◽  
Numerical Tests ◽  
Gauss Quadrature Formula ◽  
Gauss Quadrature Rules

AbstractThis paper is concerned with the numerical approximation of Fredholm integral equations of the second kind. A Nyström method based on the anti-Gauss quadrature formula is developed and investigated in terms of stability and convergence in appropriate weighted spaces. The Nyström interpolants corresponding to the Gauss and the anti-Gauss quadrature rules are proved to furnish upper and lower bounds for the solution of the equation, under suitable assumptions which are easily verified for a particular weight function. Hence, an error estimate is available, and the accuracy of the solution can be improved by approximating it by an averaged Nyström interpolant. The effectiveness of the proposed approach is illustrated through different numerical tests.

A Regularizing Parameter for Some Fredholm Integral Equations

2010 ◽  
Vol 10 (2) ◽  
pp. 177-194
Author(s):  
L. Fermo
Keyword(s):  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Numerical Tests

AbstractThe regularizing parameter appearing in some Fredholm integral equations of the second kind is discussed. Theoretical estimates and the results of numerical tests confirming the theoretical expectations are given.

scholarly journals Solving second kind linear Fredholm integral equations via Quarter-Sweep SOR iterative method

2014 ◽  
Vol 6 (2) ◽  
Author(s):  
Mohana Sundaram Muthuvalu ◽  
Jumat Sulaiman
Keyword(s):  
Iterative Method ◽  
Linear Systems ◽  
Integral Equations ◽  
Numerical Solutions ◽  
Fredholm Integral Equations ◽  
Quadrature Method ◽  
Numerical Tests ◽  
Successive Over Relaxation

In this paper, we consider the numerical solutions of linear Fredholm integral equations of the second kind. The Quarter-Sweep Successive Over-Relaxation (QSSOR) iterative method is applied to solve linear systems generated from discretization of the second kind linear Fredholm integral equations using quadrature method. In addition, the formulation and implementation of the proposed method to solve the problem are also presented. Numerical tests and comparisons with other existing methods are given to illustrate the effectiveness of the proposed method.

scholarly journals An Ulm-Type Inverse-Free Iterative Scheme for Fredholm Integral Equations of Second Kind

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1957
Author(s):  
José M. Gutiérrez ◽  
Miguel Á. Hernández-Verón
Keyword(s):  
Integral Equations ◽  
Order Of Convergence ◽  
Iterative Scheme ◽  
Semilocal Convergence ◽  
Fredholm Integral Equations ◽  
Linear Integral ◽  
Ulm’S Method ◽  
Theoretical Results ◽  
Quadratic Order ◽  
Linear Integral Equations

In this paper, we present an iterative method based on the well-known Ulm’s method to numerically solve Fredholm integral equations of the second kind. We support our strategy in the symmetry between two well-known problems in Numerical Analysis: the solution of linear integral equations and the approximation of inverse operators. In this way, we obtain a two-folded algorithm that allows us to approximate, with quadratic order of convergence, the solution of the integral equation as well as the inverses at the solution of the derivative of the operator related to the problem. We have studied the semilocal convergence of the method and we have obtained the expression of the method in a particular case, given by some adequate initial choices. The theoretical results are illustrated with two applications to integral equations, given by symmetric non-separable kernels.

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