# Fredholm integral equations

## Fredholm integral equations

[′fred‚hōm ¦int·ə·grəl i′kwā·zhənz]
(mathematics)
Given functions ƒ(x) and K (x, y), the Fredholm integral equations with unknown function y are
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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As future researches, we can use finite and divided differences methods, fuzzy spline interpolation, and fuzzy quasi-interpolation for solving two-dimensional linear or nonlinear fuzzy Fredholm integral equations.
These equations are considered the Fredholm integral equations of the first kind with respect to the normal derivative qi on the interface [psi].sub.1] and to the normal derivative [[??].sub.3] on the interface [psi].sub.2], respectively.
Yousefi, "The approximate solution of a class of Fredholm integral equations with a logarithmic kernel by using Chebyshev polynomials," Global Journal of Computer Sciences, vol.
Ghasemi, "A novel computing multi-parametric homotopy approach for system of linear and nonlinear Fredholm integral equations," Applied Mathematics and Computation, vol.
Ghanbari, "Variational iteration method for solving Voltarra and Fredholm integral equations of the second kind," General Mathematics Notes, vol.
Then ([[mu].sub.1], [[mu].sub.2]) [member of] [W.sub.1] x [W.sub.2] is a solution of (12), if and only if ([[mu].sub.1], [[mu].sub.2]) [member of] [W.sub.1] x [W.sub.2] is a solution of system of Fredholm integral equations (4).
Loghmani, "Numerical solution of Fredholm integral equations of the second kind by using integral mean value theorem," Applied Mathematical Modelling, vol.
Iqbal, "Optimal homotopy asymptotic method for solving nonlinear Fredholm integral equations of second kind," Applied Mathematics and Computation, vol.
Iqbal, Optimal homotopy asymptotic method for solving nonlinear Fredholm integral equations of second kind, Appl.
He covers introductory concepts, Fredholm integral equations, Volterra integral equations, Fredholm integro-differential equations, Volterra integro-differential equations, singular integral equations, nonlinear Fredholm integral equations, nonlinear Volterra integral equations, and applications of integral equations.
Example 2 Use the above method to obtain an approximate solution of the Fredholm integral equations
Doumanidis, "Approximate solution to Fredholm integral equations using linear regression and applications to heat and mass transfer," Engineering Analysis with Boundary Elements, vol.

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