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11 Jun 2024: Analysis of collocation methods for Fredholm integral equations. In collaboration with Prof. ... Convergence analysis of least-squares oversampled collocation methods for Fredholm integral equations.

15 Jun 2024: 2011). 1. (doi: 10.1109/mlsp.2011.6064632). The computation of the spectra of highly oscillatory Fredholm integral operators. ... H Brunner, A Iserles, SP Norsett. – Journal of Integral Equations and Applications.

5 Dec 2023: problem, approximation in L1 vs L2. 5. Fredholm Theory and linear integral equations.

v1(0) = 1, v2(0) = 0,. or the system of Volterra integral equations. ... 6 Chebyshev polynomial approximations. of second kind Fredholm integral equations with symmetric kernel containingMacDonald’s function of the complex order K1/2iτ (x).

17 Jun 2019: Gravity g acts vertically and surface tension is negligible. Assuming that the horizontal velocity component u and pressure p satisfy thelubrication equations. ... 17C Mathematical Methods. (i) State the Fredholm alternative for Fredholm integral

10 Apr 2008: 2000 Mathematics Subject Classification: Primary: 45C05; Secondary: 65R20,45M05. Keywords: Complex-symmetric Fredholm integral operator, highly oscillatory kernel,asymptotic behaviour of spectrum, Fredholm integral equations, asymptotic behaviour

13] V. S. Rabinovich and S. Roch: The Fredholm index of locally compactband-dominated operators on Lp(R), Integral Equations and Operator Theory,57 (2007), 263–281. ... 14] V. S. Rabinovich, S. Roch and J. Roe: Fredholm indices of

26 Mar 2011: Iserles, and S. P. Nørsett, The spectral problem for a class ofhighly oscillatory Fredholm integral equations. ... J. Integral Equations Appl.,to appear. [11] J. A. Cochran, The existence of eigenvalues for the integral equations of lasertheory.

a number of one-parameter models, we start with the following lemma, which results in thetheory of Fredholm-Volterra integral equations [see Mason and Handscomb(2002), Ch. ... H(u,v) =1. |u v|α(1 v2)(1α)/2.(4.9). It appears in the theory of

6 Dec 2020: Mathematics Subject Classification (2010): 47A10, 65J10, 46N40, 03D55. 1 IntroductionSpectral computations are ubiquitous in the sciences with applications in solutions to differential and in-tegral equations, spline functions, orthogonal polynomials

17 Jun 2019: Show that the solution to the approximate equations is given by a streamfunctionψ proportional to P. ... eiu2du =. πeiπ/4.]. Part II 2002. 26. A3/17 Mathematical Methods. (i) State the Fredholm alternative for Fredholm integral equations of the second

28 Feb 2012: Integral equations. Fredholm equations can be approximated by a variety of techniques (Atkinson 1997).Finite differences are a popular option: thus, for example, 1. ... Another problem associated with Fredholm equations is the calculation of thespectrum

29 Jan 2019: Mathematics Subject Classification (2010): 47A10, 65J10, 46N40, 03D55. 1 IntroductionSpectral computations are ubiquitous in the sciences with applications in solutions to differential and in-tegral equations, spline functions, orthogonal polynomials

First, we discuss this for a pure scattering problem and re-lated indirect boundary integral equations. ... couple the boundary integral equations (20) together with the variational problem on , we finally.

1 May 2024: Numerical experiments are includedfor the two-dimensional Helmholtz equation. Keywords Fredholm Integral Equations Collocation Methods Least-squares oversampling Convergence Analysis. ... In the present work, we are interested in the study of

It was used by. 1.2. A BRIEF HISTORY 13. Anselone for the convergence analysis of approximation methods like the Nyströmmethod for second kind integral equations. ... Other applications included thestudy of multidimensional Wiener-Hopf operators and,

12 Nov 2010: 279] made alreadyin [8]: ”The analysis of integral equations with general complex-symmetric kernels remains, atpresent, an art form in which each separate equation appears to necessitate treatment basedalmost solely on ... Specifically, the eigenvalues

30 Jul 2010: J.Integral Equations Appl. 6 (1994), 267–301. [7] A. Böttcher, H. Brunner, A. ... 11] H. Brunner, A. Iserles, and S. P. Nørsett, The computation of the spectra of highlyoscillatory Fredholm integral operators.

17 Mar 2010: Widom, Two remarks on spectral approximations forWiener–Hopf operators. J. Integral Equations Appl. ... P. Nørsett, The computation of the spectra ofhighly oscillatory Fredholm integral operators.

27 Apr 2019: Other ways to treat boundary integral equations in cracked domainscan be found in [49,50]. ... Choosing the Green’s function that satisfies ahomogeneous Dirichlet boundary condition on the x-axis, the boundary integral equations giverise to the