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An adaptive hybrid quadrature scheme: Combining Simpson's rule and Gaussian quadrature for enhanced numerical integration. [PDF]
PLoS ONEThis study develops a novel adaptive hybrid quadrature that combines Simpson's 1/3 rule with Gauss-Legendre quadrature to overcome the classical difficulties in performing numerical integration.
Abadi Abraha Asgedom +1 more
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Rational averaged gauss quadrature rules [PDF]
Filomat, 2020 It is important to be able to estimate the quadrature error in Gauss rules. Several approaches have been developed, including the evaluation of associated Gauss-Kronrod rules (if they exist), or the associated averaged Gauss and generalized averaged Gauss rules.
Lothar Reichel +2 more
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A Perturbed Milne’s Quadrature Rule for n-Times Differentiable Functions with Lp-Error Estimates
Axioms, 2023 In this work, a perturbed Milne’s quadrature rule for n-times differentiable functions with Lp-error estimates is derived. One of the most important advantages of our result is that it is verified for p-variation and Lipschitz functions.
Ayman Hazaymeh +4 more
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Anti-Szego quadrature rules [PDF]
Mathematics of Computation, 2006 The authors purpose a new class of discretization methods for approximating integrals on an interval of \(2\pi\)-length. The integrand contains a periodic function and the derivative of a measure function. The purposed discretization methods are called anti-Szegő quadrature rules.
Kim, Sun-Mi, Reichel, Lothar
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DEVELOPMENT AND TESTING OF THE MODIFIED SIMPSON’S RULE FOR DISCRETE ORDINATES TRANSPORT APPLICATIONS [PDF]
EPJ Web of Conferences, 2021 A new angular quadrature type termed Modified Simpson Trapezoidal (MST) is developed based on the conventional Simpson’s 1/3 rule where the angular pattern over polar levels has a trapezoid shape. An adaptive coefficient correction scheme is developed to
Hu Xiaoyu, Azmy Yousry Y.
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Some Generalized Error Inequalities and Applications
Journal of Inequalities and Applications, 2008 We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's 3/8, and Lobatto four-point quadrature rule for twice-differentiable mapping.
Nazir Ahmad Mir, Fiza Zafar
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Calculation of Gauss Quadrature Rules [PDF]
Mathematics of Computation, 1969 Several algorithms are given and compared for computing Gauss quadrature rules. It is shown that given the three term recurrence relation for the orthogonal polynomials generated by the weight function, the quadrature rule may be generated by computing the eigenvalues and first component of the orthornormalized eigenvectors of a symmetric tridiagonal ...
Golub, Gene H., Welsch, John H.
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On Appel-Type Quadrature Rules [PDF]
gmj, 2002 Abstract The Radon technique is applied in order to recover a quadrature rule based on Appel polynomials and the so called Appel numbers. The relevant formula generalizes both the Euler-MacLaurin quadrature rule and a similar rule using Euler (instead of Bernoulli) numbers and even (instead of odd) derivatives of the given function at ...
BELINGERI, Carlo, GERMANO, Bruna
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Stress-driven Approach to Vibrational Analysis of FGM Annular Nano-plate based on First-order Shear Deformation Plate Theory [PDF]
Journal of Applied and Computational Mechanics, 2023 Vibrational behavior of small-scale functionally graded annular plate based on the first-order shear deformation theory, and non-local stress-driven model is investigated.
Mojtaba Shariati +2 more
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Szegő Quadrature Kalman Filter for Oscillatory Systems
IEEE Access, 2020 Filtering problems with oscillatory system dynamics commonly appear in real-life. However, the existing Gaussian filters, like the unscented Kalman filter (UKF), cubature Kalman filter CKF, Gauss-Hermite filter (GHF) and cubature quadrature Kalman filter
Abhinoy Kumar Singh
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