• 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
  • Thumbnail for Erik Ivar Fredholm
    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
  • Thumbnail for Rendering equation
    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
  • Thumbnail for Method of moments (electromagnetics)
    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
  • Thumbnail for Green's function
    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
  • Thumbnail for Large eddy simulation
    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