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...

Department of Mathematics, University of Gaziantep, Gaziantep, Turkey e-mail address : [email protected] Abstract For the practical estimation of the error of Gauss quadrature rules Gauss-Kronrod rules are widely used; but, it is well known that for the generalized Hermite weight function, ωα(x) = |x|2α exp(−x2) over [−∞,∞], real positive Gauss-Kronrod rules do not exist. Among the alternati...

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...

Block error rate performance of subcarrier intensity modulation based optical wireless communication systems is analysed over Gamma–Gamma and lognormal atmospheric turbulence channels. The analysis is applicable to non-coherent binary modulations and coherent binary phase shift keying. The special cases of K-distributed strong turbulence channel and negative exponential turbulence channel are a...

We study Gauss-Kronrod quadrature formulae for the Jacobi weight function «/"'"'(t) = (l-i)Q(l + t)'3 and its special case a = ß = X^ of the Gegenbauer weight function. We are interested in delineating regions in the (a, /3)-plane, resp. intervals in A, for which the quadrature rule has (a) the interlacing property, i.e., the Gauss nodes and the Kronrod nodes interlace; (b) all nodes contained ...

Here, Jc F[x]w(dx) denotes the Wiener integral, and / F[0(u, ■ )]v(du) denotes an integral over some Euclidean space. In [1] Cameron determined a pair (v, 0) by imposing on (1.2) the condition that the formula be exact for polynomial functionals of degree ^3. Imposing the same requirement, Vladimirov [5] constructed a family of pairs (v, 6). In this paper we shall develop a class of approximati...

A main class of inequalities including generalized Ostrowski and Ostrowski-Grüss inequalities is established in ] , [ 1 b a L and ] , [ b a L spaces. As this class can be corresponded to a weighted approximation formula, new inequalities can be obtained by using its upper and lower bounds. Some illustrative examples such as three new generalizations of Ostrowski and Ostrowski-Grüss inequalities...