On relation between one multiple and a corresponding one-dimensional integral with applications [PDF]
Yugoslav Journal of Operations Research, 2018 For a given finite positive measure on an interval I ⊆ R, a multiple stochastic integral of a Volterra kernel with respect to a product of a corresponding Gaussian orthogonal stochastic measure is introduced.
Bajić Tatjana
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Some orthogonal polynomials on the finite interval and Gaussian quadrature rules for fractional Riemann‐Liouville integrals [PDF]
Mathematical Methods in the Applied Sciences, 2020 Inspired with papers by Bokhari, Qadir, and Al‐Attas (2010) and by Rapaić, Šekara, and Govedarica (2014), in this paper we investigate a few types of orthogonal polynomials on finite intervals and derive the corresponding quadrature formulas of Gaussian type for efficient numerical computation of the left and right fractional Riemann‐Liouville ...
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High-order, Dispersionless "Fast-Hybrid" Wave Equation Solver. Part I: $\mathcal{O}(1)$ Sampling Cost via Incident-Field Windowing and Recentering [PDF]
, 2020 This paper proposes a frequency/time hybrid integral-equation method for the time dependent wave equation in two and three-dimensional spatial domains.
Anderson, Thomas G. +2 more
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OPERATOR METHOD IN THE SCALAR WAVE DIFFRACTION BY AXIALLY-SYMMETRIC DISCONTINUITIES IN THE SCREEN
Radio Physics and Radio Astronomy, 2018 Purpose: The scalar wave diffraction by the annular slot in an infinitely thin screen is considered in case of Dirichlet and Neumann boundary conditions. Diffraction problem by a flat ring is also considered as a dual one.
M. E. Kaliberda +2 more
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A Gaussian quadrature rule for oscillatory integrals on a bounded interval
Discrete & Continuous Dynamical Systems - A, 2014 We investigate a Gaussian quadrature rule and the corresponding orthogonal polynomials for the oscillatory weight function $e^{iωx}$ on the interval $[-1,1]$. We show that such a rule attains high asymptotic order, in the sense that the quadrature error quickly decreases as a function of the frequency $ω$. However, accuracy is maintained for all values
Asheim, Andreas +3 more
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Design of quadrature rules for Müntz and Müntz-logarithmic polynomials using monomial transformation [PDF]
, 2009 A method for constructing the exact quadratures for Müntz and Müntz-logarithmic polynomials is presented. The algorithm does permit to anticipate the precision (machine precision) of the numerical integration of Müntz-logarithmic polynomials in terms of ...
Abramowitz +40 more
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The influence of random element displacement on DOA estimates obtained with (Khatri-Rao-)root-MUSIC [PDF]
, 2014 Although a wide range of direction of arrival (DOA) estimation algorithms has been described for a diverse range of array configurations, no specific stochastic analysis framework has been established to assess the probability density function of the ...
Inghelbrecht, Veronique +3 more
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MathematicsGaussian quadrature rules are commonly used to approximate integrals with respect to a non-negative measure dσ^. It is important to be able to estimate the quadrature error in the Gaussian rule used.
Dušan Lj. Djukić +5 more
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An Efficient Quadrature Rule for Highly Oscillatory Integrals with Airy Function
MathematicsIn this work, our primary focus is on the numerical computation of highly oscillatory integrals involving the Airy function. Specifically, we address integrals of the form ∫0bxαf(x)Ai(−ωx)dx over a finite or semi-infinite interval, where the integrand ...
Guidong Liu, Zhenhua Xu, Bin Li
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, 2010 Effective modeling and numerical spectral-based propagation schemes are proposed for addressing the challenges in time-dependent quantum simulations of systems ranging from atoms, molecules, and nanostructures to emerging nanoelectronic devices.
Chen, Zuojing, Polizzi, Eric
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