In this paper we examine the computation of the potential generated by space-time BIE representations associated with Dirichlet and Neumann problems for the 2D wave equation. In particular, we consider the efficient evaluation of the (convolution) time integral that appears in the potential representation. For this, we propose two simple quadrature rules which appear more efficient than the cur...

Abstract We analyse the Gaussian wave packet transform. Based on Fourier inversion formula and a partition of unity, which is formed by collection basis functions, new representation square-integrable functions presented. Including rigorous error analysis, variants transform are then derived discretization integral via different quadrature rules. Gauss–Hermite quadrature, we introduce packets i...

We consider a Gaussian type quadrature rule for some classes of integrands involving highly oscillatory functions of the form f (x) = f 1 (x) sin ζ x + f 2 (x) cos ζ x, where f 1 (x) and f 2 (x) are smooth, ζ ∈ R. We find weights σ ν and nodes x ν , ν = 1, 2,. .. , n, in a quadrature formula of the form 1 −1 f (x) dx ≈ n ν=1 σ ν f (x ν) such that it is exact for all polynomials f 1 (x) and f 2 ...

Many problems of operations research or decision science involve continuous probability distributions, whose handling may be sometimes unmanageable; in order to tackle this issue, different forms approximation methods can used. When constructing a k-point discrete random variable, moment matching, i.e., matching as many moments possible the original distribution, is most popular technique. This...

We present a numerical code for the computation of nodes and weights low-cardinality positive quadrature formula on spherical triangles, nearly exact polynomials given degree. The algorithm is based subperiodic trigonometric Gaussian planar elliptical sectors Caratheodory–Tchakaloff compression via NNLS.

This paper provides a rigorous and delicate analysis for exponential decay of Jacobi polynomial expansions of analytic functions associated with the Bernstein ellipse. Using an argument that can recover the best estimate for the Chebyshev expansion, we derive various new and sharp bounds of the expansion coefficients, which are featured with explicit dependence of all related parameters and val...

A new numerical method for solving the kinetic collection equation (KCE) is proposed, and its accuracy and convergence are investigated. The method, herein referred to as the bin integral method with Gauss quadrature (BIMGQ), makes use of two binwise moments, namely, the number and mass concentration in each bin. These two degrees of freedom define an extended linear representation of the numbe...

This paper presents a Gauss Legendre quadrature method for numerical integration over the standard triangular surface: {(x, y) | 0 , 1, 1} x y x y ≤ ≤ + ≤ in the Cartesian two-dimensional (x, y) space. Mathematical transformation from (x, y) space to (ξ, η) space map the standard triangle in (x, y) space to a standard 2-square in (ξ, η) space: {(ξ, η)|–1 ≤ ξ, η ≤ 1}. This overcomes the difficul...

Abstract. Let dμ be a nonnegative measure with support on the real axis and let α ∈ R be outside the convex hull of the support. This paper describes a new approach to determining recursion coefficients for Gauss quadrature rules associated with measures of the form dμ̌(x) := dμ(x)/(x − α)2l. The proposed method is based on determining recursion coefficients for a suitable family of orthonormal ...

We propose and analyse a fully discrete Petrov–Galerkin method with quadrature, for solving second-order, variable coefficient, elliptic boundary value problems on rectangular domains. In our scheme, the trial space consists of C2 splines of degree r 3, the test space consists of C0 splines of degree r − 2, and we use composite (r − 1)-point Gauss quadrature. We show existence and uniqueness of...