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26 Jun 2024: Opportunities. The Fredholm Factorization Method Directly Applied to Generalized Wiener-Hopf Equations. ... The technique is combined with special complex mapping to transform GWHEs into Classical Wiener-Hopf equations.

26 Jun 2024: the solution of rapidly oscillating ordinary differential equations, computation of spectra of Fredholm operators with highly oscillatory kernels and rapid approximation of functions by Birkhoff series. ... Publications. Stability and Asymptotic

26 Jun 2024: the solution of rapidly oscillating ordinary differential equations, computation of spectra of Fredholm operators with highly oscillatory kernels and rapid approximation of functions by Birkhoff series. ... Publications. Stability and Asymptotic

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.

26 Jun 2024: the solution of rapidly oscillating ordinary differential equations, computation of spectra of Fredholm operators with highly oscillatory kernels and rapid approximation of functions by Birkhoff series. ... Publications. Stability and Asymptotic

17 Nov 2010: 60. Iserles. Numerical methods for differential equations in Lie groups. 61. ... Iserles. The computation of Fredholm spectra. 62. Jozsa. Classical simulation of quantum computations.

Consider the system of two second order differential equations (k = 2) inmore detail. ... 6 Chebyshev polynomial approximations. of second kind Fredholm integral equations with symmetric kernel containingMacDonald’s function of the complex order

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

26 Jun 2024: The Fredholm Factorization Method Directly Applied to Generalized Wiener-Hopf Equations.

26 Jun 2024: The computation of the spectra of highly oscillatory fredholm integral operators. ... H Brunner, A Iserles, SP Norsett. – Journal of Integral Equations and Applications.

16 Oct 2007: 2.1. Governing equations. In general, regions of the porous medium may only be partially saturated by thewetting liquid (water), leaving some residual air saturation. ... 250 D. Vella and H. E. Huppert. C. Upon discretizing the contour C, (3.3) gives

21 May 2005: Prove the Fredholm alternative: Letλ R, λ 6= 0, and let x0 H. ... Consider the equations. Tx = λx (1). Tx = λx x0 (2).

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

22 Feb 2024: Singh, "Efficient methods for time-dependence in semiclassical Schrödinger equations", Proc. Royal Soc. ... Nørsett, "The spectral problem for a class of highly oscillatory Fredholm differential equations" IMA J.

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 Jan 2017: NA2008/05: Hermann Brunner, Arieh Iserles & Syvert Nørsett, "The spectral problem for a class of highly oscillatory Fredholm differential equations". ... NA2004/02: Arieh Iserles, "On the method of Neumann series for highly oscillatory equations".

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

10 Apr 2008: Therange of issues that we wish eventually to bring under scrutiny include spectral problemsfor Fredholm operators, and also the solution of Fredholm and Volterra equations, all withhighly oscillatory kernels. ... 9406). They alsowish to acknowledge

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

dimension n = 3 an alternative set of equations can be obtained byintroducing the twist potential ω. ... Our choice of those terms arisesfrom harmonic coordinates for the vacuum Einstein equations in one dimen-sion higher.

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.

diffusion equations on M with an explicit lowerbound on the zero-order term c. ... 25. [14] G. M. Lieberman. Second order parabolic differential equations. World Scientific Publishing(1996).

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

17 Mar 2010: Widom, Two remarks on spectral approximations forWiener–Hopf operators. J. Integral Equations Appl. ... Nørsett, The spectral problem for a classof highly oscillatory Fredholm differential equations.

32, Sect. 4] for Maxwell equations). 12 FEM-BEM Coupling for Maxwell Transmission Problems. ... Recalling the Calderón projector in its operator form, we arrive at the followingtwo equations.

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

If C is semi-Fredholm then α(C) β(C) is called theindex of C. ... 899) that L is Fredholm iff all the limitoperators of L are invertible.

25 Oct 2018: ential equations inside a compact domain Rn. But our approach should leave youwith many questions. ... Green's Functions for Ordinary Differential Equations. The Fredholm Alternative. Green's functions.

26 Nov 2016: as the method of characteristics, which you met first in 1A Differential Equations. ... Green's Functions for Ordinary Differential Equations. The Fredholm Alternative. Green's functions.

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

12 Nov 2010: Specifically, the eigenvalues are λ = a(x), where x satisfiesone of the equations. ... ϕτ (t) = (1 iω)eiωt (1 iω)eiωt. (2.8). Now note that equation (2.3) is equivalent to the satisfaction of one of the two equations.

23 Jan 2004: that. ‖K‖ 14 ‖etÃF̃ etÃ‖h2 O(h3).(2.1)Therefore ‖K‖ scales with h2, rather than with h in standard applications ofNeumann expansions to, say, Fredholm equations of the second ... 561–599. 10. , Think globally, act locally: Solving

30 Jul 2010: described, then for W(aλ)to be Fredholm it is necessary that |ϕ(ξ)| = O(log |ξ|) as |ξ|. ... J.Integral Equations Appl. 6 (1994), 267–301. [7] A. Böttcher, H. Brunner, A.

26 Jul 2013: The linearity of the Stokes equations allows f the introduction and exploitation ofGreen’s functions. ... Derivatives of the Stokeslet singularityproduce other higher-order singularity solutions of the Stokes equations.

21 Sep 2005: Evenmore ambitious goal is the analysis of highly oscillatory Fredholm equationsof the second kind. ... Oscillatory Integrals, Princeton University Press, Princeton, NJ.Ursell, F. (1969), ‘Integral equations with a rapidly oscillating kernel’, J.

27 Apr 2019: This enables us to write the Helmholtz, modified Helmholtzand Laplace equations, respectively, in the form. ... Choosing the Green’s function that satisfies ahomogeneous Dirichlet boundary condition on the x-axis, the boundary integral equations