
	Where results make sense

Topic: Fredholm integral equation

Related Topics

Neumann boundary condition

In the News (Fri 25 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Integral equation - Wikipedia, the free encyclopedia
		In mathematics, an integral equation is an equation in which an unknown function appears under an integral sign.
		There is a close connection between differential and integral equations, and some problems may be formulated either way.
		Problems in which integral equations are encountered include radiative energy transfer and the oscillation of a string, membrane, or axle.
	en.wikipedia.org /wiki/Integral_equation (301 words)

	Fredholm integral equation - Wikipedia, the free encyclopedia
		In this case that is supported by a computational theory, including the Fredholm determinants.
		An inhomogeneous Fredholm equation of the second kind is essentially a form of the eigenvalue problem for the above equation:
		Integral Equations at EqWorld: The World of Mathematical Equations.
	en.wikipedia.org /wiki/Fredholm_integral_equation (205 words)

	Encyclopedia: Integral equation
		In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables.
		Maxwells equations are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter.
		The most basic type of integral equation is a Fredholm equation of the first type: In mathematics, the Fredholm integral equation introduced by Ivar Fredholm gives rises to a Fredholm operator.
	www.nationmaster.com /encyclopedia/Integral-equation (669 words)

	Fredholm (Site not responding. Last check: 2007-10-19)
		He solved his operator equation in the particular cases which arise in the study of the physical problem in his thesis (and in the paper which appeared in 1900 based on that thesis) while the general case was solved by Fredholm somewhat later and not published until 1908.
		Fredholm's work on integral equations was met with great interest and boosted the morale and self-respect of Swedish mathematicians who so far had been working under the shadow of the continental cultural empires Germany and France.
		Fredholm received many honours for his mathematical contributions, including the V A Wallmarks Prize for the theory of differential equations in 1903, the Poncelet Prize from the French
	www-groups.dcs.st-and.ac.uk /~history/Mathematicians/Fredholm.html (1619 words)

	Compact operator - Wikipedia, the free encyclopedia
		The origin of the theory of compact operators is in the theory of integral equations.
		A typical Fredholm integral equation gives rise to a compact operator K on function spaces; the compactness property is shown by equicontinuity.
		The abstract idea of Fredholm operator is derived from this connection.
	en.wikipedia.org /wiki/Compact_operator (475 words)

	Expert About fr:Fredholm
		Linear Volterra integral equations are re-written as Fredholm integral equations with appropriately modified kernels.
		The Fredholm determinant for a Dirac operator appropriate to a particle moving in one spatial dimension is investigated.
		The relation between the Fredholm determinant and the finite determinant was conjectured in an earlier work by D. DC MetaData for: On the Fredholm ontegral equation for the two-and three-dimensional heat radiation problem.
	expertsite.biz /dir/fr/Fredholm.htm (815 words)

	[No title]
		This dissertation is an examination of the application of the boundary integral equation method to describe axi-symmetric particle motion in Stokes flow.
		The axi-symmetric integral equations are two-dimensional, linear and exhibit a logarithmic singularity via the presence of complete elliptic integrals of the first and second kind.
		The first is a theoretical investigation of Fredholm integral equations of the first kind and the second part is a study of numerical techniques to simulate axi-symmetric particle (rigid and drop) dynamics in Stokes flow.
	rgmia.vu.edu.au /monographs/johnr.html (693 words)

	High-Resolution Electromagnetic Imaging of the Conductive Earth Interior -- from Mathematica Information Center
		However, a clue for high-resolution imaging in the diffusive approximation is given by a Fredholm integral equation of the first kind which links diffusive fields to their propagative duals.
		If these duals could be recovered by inverting this integral equation, the seismic imaging toolbox might be used, at least from a theoretical point of view, to produce fine electromagnetic images.
		Spectral decomposition of the integral operator shows that the inverse problem is numerically ill-posed for both noisy and/or incomplete data.
	library.wolfram.com /infocenter/Articles/2879 (235 words)

	KLUEDO - On an Integral Equation Model for Slender Bodies in Low Reynolds-Number Flows
		The interation of particular slender bodies with low Reynolds-number flows is in the limit 'slenderness to 0' described by a linear Fredholm integral equation of the second kind.
		The integral operator of this equation has a denumerable set of polynomial eigenfunctions whose corresponding eigenvalues are non-positive and of logarithmic growth.
		A spectral analysis of the integral operator restricted to an appropriate class of analytic functions is performed.
	kluedo.ub.uni-kl.de /Mathematik/Metadaten/gruen_219.html (183 words)

	Fredholm, Erik Ivar (Site not responding. Last check: 2007-10-19)
		Fredholm was born in Stockholm and studied at the Polytechnic Institute there, and at the University of Uppsala.
		Fredholm founded much of his theory on work carried out by US astronomer George Hill (1838-1914), who used linear equations involving determinants of an infinite number of rows and columns.
		In Fredholm's paper Sur une nouvelle méthode pour la résolution du problème de Dirichlet 1900, he first developed the essential part of the theory of what is now known as Fredholm's integral equation; further, he went on to define and solve the Fredholm equation of the second type, involving a definite integral.
	cartage.org.lb /en/themes/Biographies/MainBiographies/F/Fredholm/1.html (165 words)

	XII. Geometry and integral operators (Site not responding. Last check: 2007-10-19)
		Such equations are called Fredholm equations of the second kind.
		Often an integral equation can be converted into a differential equation or vice versa, so many of the laws of nature which we think of as differential equations might just as well have been developed as integral equations initially.
		In this course integral operators will be called upon to solve differential equations, and this is one of their main uses.
	www.math.gatech.edu /~harrell/pde/green/g12.html (1565 words)

	Fredholm operator -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		The abstract structure of Fredholm's theory (if not the computational aspects) can now be derived in terms of the (Click link for more info and facts about spectral theory) spectral theory of Fredholm operators on (A metric space that is linear and complete and (usually) infinite-dimensional) Hilbert space.
		This reverses history, in the sense that (German mathematician (1862-1943)) David Hilbert abstracted 'Hilbert space' in association with research on integral equations prompted by Fredholm's (amongst other things).
		The use of Fredholm operators in (A differential equation involving a functions of more than one variable) partial differential equations is an abstract form of the parametrix method.
	www.absoluteastronomy.com /encyclopedia/f/fr/fredholm_operator.htm (341 words)

	DAM: Seminars for Jan 22 - Jan 26, 2001 (Site not responding. Last check: 2007-10-19)
		Abstract: The solvability of the linear Fredholm integral equation of the first kind, both in discretized and continuous forms, is studied by certain nonlinear techniques.
		For spectrometric integral equations, this system is shown to be a nonlinear dual iterative search process.
		In the continuous setting for the integral equation, we show that a variational perturbation of the kernel, in a certain (nonlinearly weighted) dual space, is capable of yielding a direct primal solution.
	www.cfm.brown.edu /cgi-bin/dam/view_seminars.cgi?Jan-22-Jan-26-2001 (217 words)

	Integral equation (Site not responding. Last check: 2007-10-19)
		The application of an integral type constitutive equation to numerical flow analyses of viscoelastic fluid in unsteady f...
		Boundary integral equations are used to tackle linear...
		Theory of functionals and of integral and integro-differential equations.
	hallencyclopedia.com /Integral_equation (438 words)

	Journal of the ACM Bibliography (Site not responding. Last check: 2007-10-19)
		On a statistical model of Strand and Westwater for the numerical solution of a Fredholm integral equation of the first kind.
		A technique for the numerical solution of certain integral equations of the first kind.
		On the numerical solution of Fredholm integral equations of the first kind by the inversion of the linear system produced by quadrature.
	theory.lcs.mit.edu /~jacm/References/strandw1968:100.html (72 words)

	Contents & Abstracts, Schedae Informaticae, Issue 11 (2002)
		A new “adsorption stochastic algorithm” (called ASA) is proposed for solving the unstable linear Fredholm integral equation of the first kind.
		The developed algorithm was applied for the calculation of the pore size distribution of activated carbons from single adsorption isotherms assuming different forms of the kernel (i.e.
		Additionally, the ASA results obtained by solving the integral equation with the ND kernel are compared with the results obtained by regularization solution of the integral equation with density functional theory (DFT) local isotherms as a kernel.
	www.ii.uj.edu.pl /Schedae/spis11.htm (847 words)

	Institute of Mathematics of National Academy of Sciences of Armenia (Site not responding. Last check: 2007-10-19)
		For improperly elliptic equation the deficiency numbers of the Dirichlet problem outside a disk are infinite.
		The existence of a solution in a finite interval with starting point fixed, whose endpoint has to be determined from the boundary conditionsis proved, and estimates that allow to construct approximate solutions are obtained.
		The aim of the paper is to reduce both problems to Fredholm equations.
	math.sci.am /Journal/2000_6.html (360 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		Subject: Re: eigenfunctions of a integral equation Date: Mon, 27 Sep 1999 20:19:16 +0100 Newsgroups: sci.math.num-analysis Keywords: homogeneous Fredholm integral equation "Moo K. Chung" wrote: > The problem is > > \int R(t,s)f(s) ds = c^2f(t) > > and need to find n-th eigenfunction corresponding to n-th eigenvalue of > decreasing order numerically.
		This is a homogeneous Fredholm integral equation of the second kind.
		This integral eigenvalue problem can be solved analytically for a class of correlation functions (R(t,s)) defined on simple domains, such as a line, square, etc. A Galerkin procedure can be used to compute the eigenparameters numerically if an analytical solution is not possible.
	www.math.niu.edu /~rusin/known-math/99/eigenfunctions (190 words)

	Research Seminar in Analysis, Mar 6, 01 (Site not responding. Last check: 2007-10-19)
		The first step in this process is the application of an integral transform to reduce the three-dimensional transport equation to a one-dimensional form.
		Next, a procedure developed by V.A. Ambarzumian is applied to convert a Fredholm integral equation of the second kind for the source function to a nonlinear integral equation for the reflection function.
		The resulting equation requires integration over the polar and azimuthal angles; hence, the equation is said to be in a double-integral form.
	web.umr.edu /~bohner/seminar/Mar6-01.html (144 words)

	Caltech Earthquake Engineering Research Laboratory Technical Reports - Piecewise linear dynamic systems with time delays
		Since the matrix kernel for this system of integral equations is separable, the integral equation can be reduced to a system of algebraic equations involving certain integral moments of the initial function.
		This Fredholm Integral Equation Method is used effectively to construct periodic solutions to piecewise linear differential-difference equations.
		The periodic solution and its stability analysis are exact in the sense that the error induced by the truncation process in the Fredholm Integral Equation Method can be made exponentially small as the size of the transfer matrix is increased.
	caltecheerl.library.caltech.edu /253 (314 words)

	Polynomial Spline Collocation Method For Nonlinear Two--Dimensional Weakly Singular Integral Equations (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		Abstract: INTRODUCTION The solution of a second kind Fredholm integral equation with weakly singular kernel is typically nonsmooth near the boundary of the domain of integration (its derivatives are unbounded, see, for example, [1-3, 5, 7-8, 10-14]).
		If one wants to obtain a high order convergence of a numerical method for these equations one has to take into account, in some way, the singular behavior of the exact solution.
		1 On weakly singular integral equations with displacement kern..
	citeseer.ist.psu.edu /47086.html (375 words)

	Fredholm
		He developed the theory of Fredholm integral equations in Sur une nouvelle méthode pour la résolution du problème de Dirichlet (1900).
		Volterra had studied some aspects of integral equations but before Fredholm little had been done.
		Fredholm wrote papers with great care and attention so he produced work of high quatity which quickly gained him a high reputation through Europe.
	202.38.126.65 /mirror/www-history.mcs.st-and.ac.uk/history/Mathematicians/Fredholm.html (169 words)

	Chapter V (Site not responding. Last check: 2007-10-19)
		DI Palermo, 1894) and culminating in the Fredholm-Hilbert theory of integral equations.
		Certainly, the convergence of Series (5) is absolute only in the one-dimensional case; in two and more dimensions, it is conditioned solely by the change in sign of the eigen-functions in the case of a suitable choice of their sequence.
		Thus, we are now concerned with an inhomogeneous equation, the left hand side of which agrees with the homogeneous equation of a free vibration.
	kr.cs.ait.ac.th /~radok/math/mat/51.htm (5077 words)

	On the Numerical Evaluation of Stress Intensity Factors for an Interface Crack of a General Shape - Helsing ... (Site not responding. Last check: 2007-10-19)
		Abstract: A numerical algorithm is presented for the problem of a crack along the interface of an elastic inclusion embedded in an elastic plane subjected to uniform stress at infinity.
		The algorithm is based on a Fredholm integral equation of the second kind and allows for fast and accurate solutions to geometries of great complexity.
		In an example crack opening displacement and stress intensity factors are computed for a crack in the interface of an inclusion with nineteen protruding arms.
	citeseer.ist.psu.edu /helsing99numerical.html (537 words)

	cruise
		The objective of the Ph.D. research is to develop numerical solution techniques for the integral equations of nuclear reactions and scattering:
		Apply this solver to the specific case of the Lippmann-Schwinger integral equation for nuclear reactions/scattering involving large numbers of degrees of freedom.
		Yet, iterative solutions of the Lippmann-Schwinger integral equation generally diverge.
	www.krellinst.org /Fellows/cruise.html (197 words)

	Numerical Verification of Size Effect Law by Cohesive Crack Model - 2002JB001884
		Note that all the variables in equation (15) are dimensionless.
		(approximated as an eigenvector) from a discrete approximation of equation (16).
		Two-dimensional finite element mesh from which crack node compliance matrix is computed (line of symmetry, dash-dotted, is at left, and crack at base propagates to the right).
	www.agu.org /pubs/sample_articles/cr/2002JB001884/9.shtml (875 words)

	[No title] (Site not responding. Last check: 2007-10-19)
		A second method for conversion to a Fredholm integral equation depends on {\em apriori} knowledge of the eigenvalues of $L$.
		Since the Greens function $g_0(x,t)$ exists, we know that \eq L^v = g \quad, \quad B^\bar{v} = 0 \endeq is equivalent to the integral equation \eq v(x)+ \int_a^b a_0(x) g_0(t,x) v(t) dt = G(x) = \int_a^b g(t) g_0(t,x) dt \endeq The result follows for $g=0$.
		Even if one cannot convert the boundary value problem into an equivalent integral equation, the necessity of the alternative theorem is still true.
	www.math.montana.edu /~pernarow/M560/2000/2ndorderBVP.texOLD (1251 words)

	The Discrete Ordinates Method For The Neutron Transport Equation In An Infinite Cylindrical Domain (ResearchIndex) (Site not responding. Last check: 2007-10-19)
		We prove a regularity result for a Fredholm integral equation with weakly singular kernel, arising in connection with the neutron transport equation in an infinite cylindrical domain.
		This result is applied in the error analysis of the discrete ordinates method for the numerical solution of the neutron transport equation.
		We derive an error estimate in the L 1 -norm for the...
	citeseer.ist.psu.edu /79759.html (366 words)

Try your search on: Qwika (all wikis)