Estimates of the error in Gauss–Legendre quadrature for double integrals

Estimates of the error in Gauss-Legendre quadrature for double integrals

Error estimates are a very important aspect of numerical integration. It is desirable to know what level of truncation error might be expected for a given number of integration points. Here, we determine estimates for the truncation error when Gauss-Legendre quadrature is applied to the numerical evaluation of two dimensional integrals which arise in the boundary element method. Two examples ar...

Quadrature Estimates for Multidimensional Integrals

We prove estimates for the error in the most straightforward discrete approximation to the integral of a compactly supported function of n variables. The methods use Fourier analysis and interpolation theory, and also make contact with classical lattice point estimates. We also prove error estimates for the approximation of the integral over an interval by the trapezoidal rule and the midpoint ...

Quadrature Rules for Fuzzy Integrals

study of cohesive devices in the textbook of english for the students of apsychology by rastegarpour

this study investigates the cohesive devices used in the textbook of english for the students of psychology. the research questions and hypotheses in the present study are based on what frequency and distribution of grammatical and lexical cohesive devices are. then, to answer the questions all grammatical and lexical cohesive devices in reading comprehension passages from 6 units of 21units th...

Some Error Estimates for the Numerical Approximation of Surface Integrals

Recently, the first author introduced a new approach to the numerical quadrature of surface integrals in the context of boundary element methods. It is assumed that a global parametrization m of the surface is only indirectly given (e.g., via an iterative method) and that m is not accessible analytically. Of particular interest are parametrizations which are based on automatic triangulations of...