Error Estimates for Gaussian Quadrature Formulae.
Error Estimates for Interpolatory Quadrature Formulae.
Error inequalities for a generalized quadrature rule.
Error inequalities for a quadrature formula of open type.
Estimation of error in approximate numerical integration near a simple pole using Chebyshev points
In this note quadrature formula with error estimate for functions with simple pole is discussed. Chebyshev points of the second kind are used as the nodes of integration.
Existence of Good Lattice Points in the Sense of Hlawka.
Extremal problems with polynomials.
Fehlerabschätzungen für Gauß-Quadraturformeln.
Fehlerabschätzungen für nichtsymmetrische Gauß-Quadraturformeln.
Finite-element discretizations of a two-dimensional grade-two fluid model
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
Finite-element discretizations of a two-dimensional grade-two fluid model
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
Functions of bounded variation, signed measures, and a general Koksma-Hlawka inequality
We prove a correspondence principle between multivariate functions of bounded variation in the sense of Hardy and Krause and signed measures of finite total variation, which allows us to obtain a simple proof of a generalized Koksma-Hlawka inequality for non-uniform measures. Applications of this inequality to importance sampling in Quasi-Monte Carlo integration and tractability theory are given. We also discuss the problem of transforming a low-discrepancy sequence with respect to the uniform measure...
Further convergence results for two quadrature rules for Cauchy type principal value integrals
New convergence and rate-of-convergence results are established for two well-known quadrature rules for the numerical evaluation of Cauchy type principal value integrals along a finite interval, namely the Gauss quadrature rule and a similar interpolatory quadrature rule where the same nodes as in the Gauss rule are used. The main result concerns the convergence of the interpolatory rule for functions satisfying the Hölder condition with exponent less or equal to . The results obtained here supplement...
Generalization of an integral formula of Guessab and Schmeisser.
Generalized Kronrod Patterson type imbedded quadratures
We present algorithms for the determination of polynomials orthogonal with respect to a positive weight function multiplied by a polynomial with simple roots inside the interval of integration. We apply these algorithms to search for and calculate all possible sequences of imbedded quadratures of maximal polynomials order of precision for the generalized Laguerre and Hermite weight functions.
Geometric sensitivity of a pinhole collimator.
Good Lattice Points Modulo Composite Numbers.
Implicit Runge- Kutta Methods for Second Kind Volterra Integral Equations.
Improvements of Euler-trapezoidal type inequalities with higher-order convexity and applications.
Indefinite integration of oscillatory functions
A simple and fast algorithm is presented for evaluating the indefinite integral of an oscillatory function , -1 ≤ x < y ≤ 1, ω ≠ 0, where the Chebyshev series expansion of the function f is known. The final solution, expressed as a finite Chebyshev series, is obtained by solving a second-order linear difference equation. Because of the nature of the equation special algorithms have to be used to find a satisfactory approximation to the integral.