A Representation for the Solution of Fredholm Integral Equations

Numerical solution of Fredholm integral equations of the first kind by using Legendre wavelets

An adaptive method for the numerical solution of Fredholm integral equations of the second kind. I. regular kernels

article Free Access Share on On the Numerical Solution of Fredholm Integral Equations of the First Kind by the Inversion of the Linear System Produced by Quadrature Author: S. Twomey U. S. Weather Bureau, Washington, D. C. U. S. Weather Bureau, Washington, D. C.View Profile Authors Info & Claims Journal of the ACMVolume 10Issue 1Jan. 1963 pp 97–101https://doi.org/10.1145/321150.321157Published:01 January 1963Publication History 721citation2,290DownloadsMetricsTotal Citations721Total Downloads2,290Last 12 Months190Last 6 weeks25 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my Alerts New Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

A modified approach to numerical solution of Fredholm integral equations of the second kind

The Numerical Solution of Integral Equations on the Half-Line

Numerial Methods for Volterra Integral Equations with Singular Kernels

In this paper, we introduce a new interpolation method that is easy to use and its interpolating function can be explicitly expressed. This interpolation method can be used for a wide spectral type of functions, since it has the ability to change the form of the interpolating function. This interpolation inspired by the Shepard type interpolation. We examine the ability of this interpolation to piecewise functions and rational functions and compare it with Lagrange interpolation and linear interpolation by using Bernstein polynomials basis. We applied this interpolation for an integral equation, and we presented a linear system of equations to approximate the solution of a Fredholm integral equation by collocation method. In the collocation method, the Reverse Interpolation expresses the approximate solution in the form of a linear combination of some basic functions. Several examples are presented to illustrate the effectiveness of the proposed method and the numerical results confirm the desired accuracy.

The use of Sherman–Morrison formula in the solution of Fredholm integral equation of second kind

Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem

Closed-form algebraic formulae are derived for the local error incurred in the numerical solution of integral equations by iterated collocation methods, the analysis being illustrated by application to Fredholm integral equations of the second kind. The novel error analysis uses an asymptotic approach, in the small parameter of the numerical mesh size, applied to a finite-rank degenerate-kernel orthogonalpolynomial approximation of the exact kernel. It is proved that, under suitable conditions, the discrepancy between our theoretically predicted error and the actual numerical error tends to zero at the rate ‖K − KM‖, where M is the rank of the degenerate-kernel approximation. A leading-order error analysis is validated on three increasingly accurate projection methods applied to both smooth and sharply peaked kernels, our error predictions being demonstrated to be exponentially convergent to experimentally obtained global numerical errors. The new method is demonstrated to be cost-effective relative to standard extrapolation.

Numerical solution of Fredholm integral equations of the first kind by using linear Legendre multi-wavelets

Information Complexity of Multivariate Fredholm Integral Equations in Sobolev Classes

In this thesis we focus on the mathematical and numerical aspects of the Fredholm integral equation of the second kind due to their wide range of physical application such as heat conducting radiation, elasticity, potential theory and electrostatics. After the classification of these integral equations we will investigate some analytical and numerical methods for solving the Fredholm integral equation of the second kind. Such analytical methods include: the degenerate kernel methods, the Adomain decomposition method, the modified decomposition method and the method of successive approximations. The numerical methods that will be presented here are: Projection methods including collocation method and Galerkin method, Degenerate kernel approximation methods and Nystrom methods. The mathematical framework of these numerical methods together with their convergence properties will be analyzed. Some numerical examples implementing these numerical methods have been obtained for solving a Fredholm integral equation of the second kind. The numerical results show a closed agreement with the exact solution.

The basic problem addressed here is that of obtaining the unknown retardation time spectrum from experimental creep response curves. The spectrum may be a set of discrete times or it may be a spectrum characterized by a continuous distribution function. The present work employs a general model which assumes that the observed creep compliance is due to the summed effect of an arbitrary distribution of mechanisms. The analysis requires the solution of Fredholm integral equations of the first kind. It is well known that this problem is ill-conditioned so that any numerical scheme will have to involve some smoothing to obtain accurate solutions. The present work employs Butler’s method of constrained regularization which takes advantage of the fact that the solution is positive and uses data-dependent smoothing. This work indicates that the imposition of the positivity constraint makes the computation of the solution much better conditioned. Computations with the method of constrained regularization employing near-optimal smoothing demonstrate its superiority over the method of Schapery for obtaining accurate solutions when the data are very noisy.

Localized adsorption on heterogeneous surfaces