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The linear barycentric rational quadrature method for Volterra integral equations [PDF]
, 2014 We introduce two direct quadrature methods based on linear rational interpolation for solving general Volterra integral equations of the second kind. The first, deduced by a direct application of linear barycentric rational quadrature given in former ...
Berrut, Jean-Paul +2 more
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Gauss–Hermite interval quadrature rule
Computers & Mathematics with Applications, 2007 Let \({\mathbf h}= (h_k)\in\mathbb{R}^n\), \(H\), \(M\), \(\varepsilon_0> 0\), \({\mathbf H}^H_n= \{{\mathbf h}\in\mathbb{R}^n\mid h_k\geq 0\), \(k=1,\dots, n\), \(\sum^n_{k=1} h_k< {\mathbf H}\}\), \({\mathbf X}_n({\mathbf h})= \{{\mathbf x}\in \mathbb{R}^n\mid -\infty< x_1- h_1\leq x_1+ h_1 0\) there exist \(\varepsilon_0> 0\) and \(M> 0\) such that ...
Milovanović, Gradimir V. +1 more
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Length Scales in Bayesian Automatic Adaptive Quadrature
EPJ Web of Conferences, 2016 Two conceptual developments in the Bayesian automatic adaptive quadrature approach to the numerical solution of one-dimensional Riemann integrals [Gh. Adam, S. Adam, Springer LNCS 7125, 1–16 (2012)] are reported.
Adam Gh., Adam S.
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Spherical Simplex-Radial Cubature Quadrature Kalman Filter
Journal of Electrical and Computer Engineering, 2017 A spherical simplex-radial cubature quadrature Kalman filter (SSRCQKF) is proposed in order to further improve the nonlinear filtering accuracy. The Gaussian probability weighted integral of the nonlinear function is decomposed into spherical integral ...
Zhaoming Li, Wenge Yang
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Gauss–Laguerre interval quadrature rule
Journal of Computational and Applied Mathematics, 2005 A Gaussian interval quadrature formula with respect to the positive weight \(w\) is a quadrature formula of the form \[ \int _a^bfw\,dx\approx \sum _{k=1}^n \frac {\mu _k}{2h_k}\int _{x_k-h_k}^{x_k+h_k}fw\,dx, \] which integrates exactly all polynomials of degree less than \(2n\).
Milovanović, Gradimir V. +1 more
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A note on a family of quadrature formulas and some applications [PDF]
Opuscula Mathematica, 2008 In this paper a construction of a one-parameter family of quadrature formulas is presented. This family contains the classical quadrature formulas: trapezoidal rule, midpoint rule and two-point Gauss rule.
Bogusław Bożek +2 more
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Application of Newton–Cotes quadrature rule for nonlinear Hammerstein integral equations [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2021 A numerical method for solving Fredholm and Volterra integral equations of the second kind is presented. The method is based on the use of the Newton–Cotes quadrature rule and Lagrange interpolation polynomials.
A. Shahsavaran
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Sparse Quadrature for High-Dimensional Integration with Gaussian Measure [PDF]
, 2017 In this work we analyze the dimension-independent convergence property of an abstract sparse quadrature scheme for numerical integration of functions of high-dimensional parameters with Gaussian measure. Under certain assumptions of the exactness and the
Chen, Peng
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Applied Sciences, 2017 An accurate and efficient Differential Quadrature Time Finite Element Method (DQTFEM) was proposed in this paper to solve structural dynamic ordinary differential equations.
Yufeng Xing, Mingbo Qin, Jing Guo
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On computation of high frequency Hankel transforms
Alexandria Engineering Journal, 2019 In this paper, we consider to compute high frequency Hankel transforms numerically. An asymptotic quadrature rule is derived based on the variable upper bound integrals. The scheme is verified to be effective by testing some numerical examples. Keywords:
Jizhong Gao, Ruyun Chen
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