This paper presents a generalized Gaussian quadrature method for numerical integration over two-dimensional bounded regions with a curved exponential edge. A general formulae for numerical integration over the regions R1 = {(x,y)|a ≤ x ≤ b, c ≤ y ≤ e} and R2 = {(x,y)|a ≤ y ≤ b, c ≤ x ≤ e} are derived, which can be directly used for integrating any type of functions over such regions. In order t...

In this report, we study in a detailed way higher order variances and quadrature Gauss Jacobi. Recall that the variance of order j measures the concentration of a probability close to j points x j,s with weight λ j,s which are determined by the parameters of the quadrature Gauss Jacobi. We shall study many example in which these measures specify adequately the distribution of probabilities. We ...

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...

To compute integrals on bounded or unbounded intervals we propose a new numerical approach by using weights and nodes of the classical Gauss quadrature rules. An account of the error and the convergence theory is given for the proposed quadrature formulas which have the advantage of reducing the condition number of the linear system arising when applying Nyström methods to solve integral equati...

The connection between convergence of product integration rules and mean convergence of Lagrange interpolation in L, (1 <p < 00) has been thoroughly analysed by Sloan and Smith [37]. Motivated by this connection, we investigate mean convergence of Lagrange interpolation at the zeros of orthogonal polynomials associated with Freud weights on R. Our results apply to the weights exp(-x”/2), m = 2,...

This paper is concerned with the hp-version of the finite element method (hp-FEM) to treat a variational inequality that models frictional contact in linear elastostatics. Such an approximation of higher order leads to a nonconforming discretization scheme. We employ Gauss-Lobatto quadrature for the approximation of the nonsmooth frictiontype functional and take the resulting quadrature error i...

In this paper, numerical spline-based differential quadrature is presented for solving the boundary and initial value problems, and its application is used to solve the fixed rectangular membrane vibration equation. For the time integration of the problem, the Runge–Kutta and spline-based differential quadrature methods have been applied. The Runge–Kutta method was unstable for solving the prob...

Orthogonal polynomials, unless they are classical, require special techniques for their computation. One of the central problems is to generate the coefficients in the basic three-term recurrence relation they are known to satisfy. There are two general approaches for doing this: methods based on moment information, and discretization methods. In the former, one develops algorithms that take as...

in the present paper, we develop a modified pseudospectral scheme for solving an optimal control problem which is governed by a switched dynamical system. many real-world processes such as chemical processes, automotive systems and manufacturing processes can be modeled as such systems. for this purpose, we replace the problem with an alternative optimal control problem in which the switching t...

Generalized averaged Gaussian quadrature formulas may yield higher accuracy than Gauss quadrature formulas that use the same moment information. This makes them attractive to use when moments or modified moments are cumbersome to evaluate. However, generalized averaged Gaussian quadrature formulas may have nodes outside the convex hull of the support of the measure defining the associated Gauss...