Results 21 to 30 of about 3,955 (267)
Gaussian quadrature rules and A-stability of Galerkin schemes for ODE
International Journal of Mathematics and Mathematical Sciences, 2003 The A-stability properties of continuous and discontinuous Galerkin methods for solving ordinary differential equations (ODEs) are established using properties of Legendre polynomials and Gaussian quadrature rules. The influence on the A-stability of the
Ali Bensebah +2 more
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A constraint on extensible quadrature rules [PDF]
Numerische Mathematik, 2015 When the worst case integration error in a family of functions decays as $n^{-α}$ for some $α>1$ and simple averages along an extensible sequence match that rate at a set of sample sizes ...
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On the Numerical Solution of a Hyperbolic Inverse Boundary Value Problem in Bounded Domains
Mathematics, 2022 We consider the inverse problem of reconstructing the boundary curve of a cavity embedded in a bounded domain. The problem is formulated in two dimensions for the wave equation.
Roman Chapko, Leonidas Mindrinos
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Variational Integrators in Holonomic Mechanics
Mathematics, 2020 Variational integrators for dynamic systems with holonomic constraints are proposed based on Hamilton’s principle. The variational principle is discretized by approximating the generalized coordinates and Lagrange multipliers by Lagrange polynomials, by ...
Shumin Man, Qiang Gao, Wanxie Zhong
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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 ...
Gradimir V. Milovanovic +1 more
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Journal of Numerical Analysis and Approximation Theory, 1983 It is shown how the construction of Gaussian quadrature rules for Cauchy type principal value integrals, as well as for finite-part integrals with an algebraic singularity, can be based on the theory of Gaussian quadrature rules for ordinary integrals ...
N. I. Ioakimidis
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Two-Point Quadrature Rules for Riemann–Stieltjes Integrals with Lp–error estimates
Moroccan Journal of Pure and Applied Analysis, 2018 In this work, we construct a new general two-point quadrature rules for the Riemann–Stieltjes integral ∫abf(t) du (t)$\int_a^b {f(t)} \,du\,(t)$, where the integrand f is assumed to be satisfied with the Hölder condition on [a, b] and the integrator u is
Alomari M.W.
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Computing Discrepancies of Smolyak Quadrature Rules
Journal of Complexity, 1996 The construction, with the tensor product technique, of the higher dimensional quadrature formulas has been developed, among others, by \textit{S. A. Smolyak} [Dokl. Acad. Nauk SSSR 148, 1042-1045 (1963; Zbl 0202.39901)]. Such a formula is obtained recursively from a sequence of 1-dimensional quadrature rules, for continuous functions in \( C([0, 1]). \
Karin Frank, Stefan Heinrich
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New Derivative Based Open Newton-Cotes Quadrature Rules
Abstract and Applied Analysis, 2014 Some new families of open Newton-Cotes rules which involve the combinations of function values and the evaluation of derivative at uniformly spaced points of the interval are presented.
Fiza Zafar +2 more
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Orthogonal polynomials and generalized Gauss-Rys quadrature formulae
Kuwait Journal of Science, 2021 Orthogonal polynomials and the corresponding quadrature formulas of Gaussian type with respect to the even weight function $\omega^{\lambda}(t;x)=\exp(-x t^2)(1-t^2)^{\lambda-1/2}$ on $(-1,1)$, with parameters $\lambda>-1/2$ and $x>0$, are considered.
Gradimir Milovanovic, Nevena Vasovic ́
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