A generalized framework is presented that extends the classical theory of finite-difference summation-by-parts (SBP) operators to include a wide range of operators, where the main extensions are i) non-repeating interior point operators, ii) nonuniform nodal distribution in the computational domain, iii) operators that do not include one or both boundary nodes. Necessary and sufficient conditio...

In this paper a numerical algorithm is proposed for the computation of the Fourier Transform. The quadrature rule developed is based on the Whittaker Cardinal Function expansion of the integrand and a certain Conformai Map. The error of the method is analyzed and numerical results are reported which confirm the accuracy of the quadrature rule.

In recent years a number of authors have considered an error analysis for quadrature rules of Newton-Cotes type. In particular, the mid-point, trapezoid and Simpson rules have been investigated more recently ([2], [4], [5], [6], [11]) with the view of obtaining bounds on the quadrature rule in terms of a variety of norms involving, at most, the first derivative. In the mentioned papers explicit...

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...

and Applied Analysis 3 The class of Runge-Kutta methods with CQ formula has been applied to delay-integro-differential equations by many authors (c.f. [18, 19]). For the CQ formula (9), we usually adopt the repeated trapezoidal rule, the repeated Simpson’s rule, or the repeated Newton-cotes rule, and so forth, denote η = max{?̃? 0 , ?̃? 1 , . . . , ?̃? m }. It should be pointed out that the adopte...

The problem of non-intrusive uncertainty quantification is studied, with a focus on two computational fluid dynamics cases. A collocation method using quadrature or cubature rules is applied, where the simulations are selected deterministically. A one-dimensional quadrature rule is proposed which is nested, symmetric, and has positive weights. The rule is based on the removal of nodes from an e...

This paper deals with an extension of one-dimensional Clenshaw–Curtis quadrature rule to R ; d P 2 on a convex domain. As one of its applications, we apply this quadrature rule to a collocation least-squares method using arbitrary abscissas for a first-order system of an elliptic boundary value problem so that the convergence analysis on a numerical solution can be shown in a standard Sobolev n...