the Fredholm integral equation is an integral equation whose solution gives rise to Fredholm theory, the study of Fredholm kernels and Fredholm operators...
8 KB (1,056 words) - 20:02, 29 March 2025
analysis, integral equations are equations in which an unknown function appears under an integral sign. In mathematical notation, integral equations may thus...
32 KB (5,605 words) - 14:20, 25 May 2025
In mathematics, the Volterra integral equations are a special type of integral equations. They are divided into two groups referred to as the first and...
8 KB (1,496 words) - 10:11, 4 June 2025
Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral...
8 KB (1,314 words) - 05:08, 14 May 2025
ways, as a theorem of linear algebra, a theorem of integral equations, or as a theorem on Fredholm operators. Part of the result states that a non-zero...
10 KB (1,464 words) - 23:00, 25 November 2024
the theory of integral equations, where integral operators supply concrete examples of such operators. A typical Fredholm integral equation gives rise to...
17 KB (2,659 words) - 02:22, 21 November 2024
Erik Ivar Fredholm (7 April 1866 – 17 August 1927) was a Swedish mathematician whose work on integral equations and operator theory foreshadowed the theory...
6 KB (524 words) - 20:09, 11 April 2025
range of factorings and rearrangements of the equation are possible. It is a Fredholm integral equation of the second kind, similar to those that arise...
13 KB (1,670 words) - 23:27, 26 May 2025
In mathematics, Fredholm's theorems are a set of celebrated results of Ivar Fredholm in the Fredholm theory of integral equations. There are several closely...
3 KB (619 words) - 22:03, 2 November 2020
Liouville–Neumann series (category Fredholm theory)
results from applying the resolvent formalism to solve Fredholm integral equations in Fredholm theory. The Liouville–Neumann series is defined as ϕ (...
2 KB (415 words) - 20:27, 2 July 2025
Method of moments (electromagnetics) (category Numerical differential equations)
\mathbf {H} _{\text{inc}}(r)} MFIE is often formulated to be a Fredholm integral equation of the second kind and is generally well-posed. Nevertheless,...
36 KB (4,009 words) - 02:45, 2 June 2025
representations. An integral transform "maps" an equation from its original "domain" into another domain, in which manipulating and solving the equation may be much...
13 KB (1,278 words) - 17:01, 18 November 2024
the idea of the Fredholm integral equation and the Fredholm operator, and are one of the objects of study in Fredholm theory. Fredholm kernels are named...
5 KB (851 words) - 16:57, 27 March 2025
Adomian decomposition method (category Differential equations)
decomposition method for nonhomogenous Fredholm integral equation of the second kind goes as follows: Given an integral equation of the form: u ( x ) = f ( x )...
25 KB (5,048 words) - 13:34, 8 July 2025
In mathematics, Carleman's equation is a Fredholm integral equation of the first kind with a logarithmic kernel. Its solution was first given by Torsten...
2 KB (363 words) - 14:42, 31 May 2017
in mathematics Fredholm determinant, in mathematics Fredholm integral equation, in mathematics Fredholm kernel, in mathematics Fredholm module, In noncommutative...
1,023 bytes (153 words) - 06:30, 19 August 2023
Yung Atmospheric Radiation K. G. Terry Hollands "The Simplified-Fredholm Integral Equation Solver and Its Use in Thermal Radiation" Michael F. Modest Radiative...
6 KB (1,330 words) - 14:47, 4 October 2024
mathematics, Fredholm operators are certain operators that arise in the Fredholm theory of integral equations. They are named in honour of Erik Ivar Fredholm. By...
10 KB (1,609 words) - 17:45, 12 June 2025
Green's function (category Differential equations)
each projection. Such an integral equation is known as a Fredholm integral equation, the study of which constitutes Fredholm theory. The primary use of...
43 KB (5,810 words) - 23:26, 15 June 2025
The Volterra equation may refer to the Volterra integral equation, an integral in the style of Fredholm theory. Product integral, an integral over an operator-valued...
262 bytes (68 words) - 23:01, 26 May 2024
Dirichlet problem (category Partial differential equations)
{\displaystyle \nu (s)} is given by the unique solution to the Fredholm integral equation of the second kind, f ( x ) = − ν ( x ) 2 + ∫ ∂ D ν ( s ) ∂ G...
14 KB (2,013 words) - 13:00, 12 June 2025
point of view the Lippmann–Schwinger equation in coordinate representation is an integral equation of Fredholm type. It can be solved by discretization...
17 KB (2,565 words) - 03:11, 13 February 2025
frequencies. Mathematically, the problem reduces to solving a Fredholm integral equation of the first kind with an ill-conditioned kernel. As a result...
8 KB (1,027 words) - 19:57, 19 June 2025
of random unitary matrices. The Fredholm determinant was first used in (Fredholm 1903) to solve an integral equation. Realizing the potential, Hilbert...
16 KB (3,227 words) - 20:07, 6 July 2025
that solving such a linear inverse problem amount to solving a Fredholm integral equation of the first kind: d ( x ) = ∫ Ω K ( x , y ) p ( y ) d y {\displaystyle...
70 KB (9,396 words) - 17:11, 5 July 2025
solving either, in the frequency domain, the convolutional integral eigenvalue (Fredholm) equation ∫ − W W D T ( ω , ω ′ ) G ( ω ′ ) d ω ′ = λ G ( ω ) , D...
20 KB (2,839 words) - 08:33, 9 July 2025
Nyström method (category Integral equations)
quadrature method seeks the numerical solution of an integral equation by replacing the integral with a representative weighted sum. The continuous problem...
3 KB (363 words) - 21:00, 14 April 2025
integral Vitali set, non-measurable set Henstock–Kurzweil integral Amenable group Banach–Tarski paradox Hausdorff paradox Fredholm equation Fredholm operator...
2 KB (221 words) - 02:51, 2 May 2022
Resolvent formalism (category Fredholm theory)
other uses, the resolvent may be used to solve the inhomogeneous Fredholm integral equations; a commonly used approach is a series solution, the Liouville–Neumann...
6 KB (871 words) - 01:13, 3 July 2024
Large eddy simulation (category Partial differential equations)
variational problem is that C {\displaystyle C} must satisfy a Fredholm integral equation of the second kind C ( x ) = f ( x ) + ∫ K ( x , y ) C ( y ) d...
45 KB (7,232 words) - 18:38, 5 March 2025