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When the worst case integration error in a family of functions decays as nfor some > 1 and simple averages along an extensible sequence match that rate at a set of sample sizes n1 < n2 <    < 1...
Gauss quadrature is a well known method for estimating the integral of a continuous function with respect to a given measure as a weighted sum of the function evaluated at a set of node points. Gauss ...
We study the error in quadrature rules on a compact manifold, XN j=1 !jf (zj) − Z M f(x)dx ≤ cD {zj} V {f} .
Following the seminal work of F. Bouchut on zero pressure gas dynamics which has been extensively used for gas particle-flows, the present contribution investigates quadrature-based velocity moments ...
In this work, we describe, analyze, and implement a pseudospec-tral quadrature method for a global computer modeling of the incompressible surface Navier-Stokes equations on the rotating unit sphere. ...
The unstable system of plasma equations where an electron beam is injected under a high-frequency electric field is reduced to the variable -coefficient unstable nonlinear Schrödinger (vcUNLS) eq...
Given are two strictly positive constants a and k. We show that if a ¸ 3:92k then there exists an open and bounded set ­ in R2 which contains strictly the line segment C (C = [¡1; 1]...
A generalization of the pre-Grüss inequality is presented. It is applied to estimations of remainders of some quadrature formulae.
The order structure of the set of six operators connected with quadrature rules is established in the class of 3-convex functions. Convex combinations of these operators are studied and their error bo...
The error bounds for Gauss-Legendre and Lobatto quadratures are proved for four times differentiable functions (instead of six times differentiable functions as in the classical results). Auxiliaril...
In the article ''N. Ujevic, A generalization of the pre-Grüss inequality and applications to some quadrature formulae, J. Inequal. Pure Appl. Math., 3(2), Art. 13, 2002'' error bounds for some quadrat...
The order structure of the set of six operators connected with quadrature rules is established in the class of 5-convex functions. An error bound of the Lobatto quadrature rule with five knots is g...
Computation of eigenvalues of regular Sturm-Liouville problems with periodic boundary conditions is considered. It is shown through numerical illustrations that both polynomial-based differential quad...

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