In this paper we develop a numerical scheme based on quadratures to approximate solutions of integro-differential equations involving convolution kernels, $$\nu $$ , diffusive type. particular, assume is symmetric and exponentially decaying at infinity. We consider problems posed in bounded domains $${\mathbb {R}}$$ . the case with nonlocal Dirichlet boundary conditions, show convergence for ke...

II THE QUANTIZED ELECTROMAGNETIC FIELD 3 A Quadratures of the electromagnetic field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 B Coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 C Squeezed states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 D Measurement of ...

We construct efficient quadratures for the integration of polynomials over irregular convex polygons and polyhedrons based on moment fitting equations. The quadrature construction scheme involves the integration of monomial basis functions, which is performed using homogeneous quadratures with minimal number of integration points, and the solution of a small linear system of equations. The cons...

A numerical integration method that has rapid convergence for integrands with known singularities is presented. Based on endpoint corrections to the trapezoidal rule, the quadratures are suited for the discretization of a variety of integral equations encountered in mathematical physics. The quadratures are based on a technique introduced by Rokhlin (Computers Math. Applic. 20, pp. 51-62, 1990)...

We present a novel theoretical approach to the analysis of adaptive quadratures and adaptive Simpson quadratures in particular which leads to the construction of a new algorithm for automatic integration. For a given function [Formula: see text] with [Formula: see text] and possible endpoint singularities the algorithm produces an approximation to [Formula: see text] within a given [Formula: se...

We present results that are a classical analog to quantum noise cancellation. It is possible to breach the standard quantum limit in an interferometer by the use of squeezing to correlate orthogonal quadratures of quantum noise, causing their effects on the resulting sensitivity to cancel. A laser beam incident on a Fabry-Perot cavity was imprinted with classical, correlated noise in the same q...

The problem of inversion the integral Laplace transform, which belongs to class ill-posed problems, is considered. Integral equations are reduced ill-conditioned systems linear algebraic (SLAE), in unknowns either expansion coefficients a series terms shifted Legendre polynomials, or approximate values desired original at number points. first step reduction SLAE apply quadrature formulas that p...