This is to certify that I have examined a copy of a technical report by Kazh Brito and found it satisfactory in all respects, and that any and all revisions required by the examining committee have been made. Abstract This is an exploration of Legendre spectral finite-element (LSFE) formulations for Reissner-Mindlin plates. The goal was to compare high-order LSFEs with standard low-order finite...

Abstract In this work, three different integration techniques, which are the numerical, semi-analytical and exact integration techniques are briefly reviewed. Numerical integrations are carried out using three different Quadrature rules, which are the Classical Gauss Quadrature, Gauss Legendre and Generalized Gaussian Quadrature. Line integral method is used to perform semi-analytical integrati...

We derive a simple accuracy matching strategy for inexact Gauss Newton methods and apply it to the numerical solution of boundary value problems of ordinary differential equations by collocation. The matching strategy is based on an affine contravariant convergence theorem, i.e., the characteristic constants are invariant under affine transformations of the domain. The inexact Gauss Newton meth...

1. Introduction. The estimation of quadrature errors for analytic functions has been considered by Davis and Rabinowitz [1]. An estimate for the error of the Gaussian quadrature formula for analytic functions was obtained by Davis [2]. McNamee [3] has also discussed the estimation of error of the Gauss-Legendre quadrature for analytic functions. Convergence of the Gaussian quadratures was discu...

While second order methods for computational simulations of fluid flow provide the basis of widely used commercial software, there is a need for higher order methods for more accurate simulations of turbulent and vortex dominated flows. The discontinuous Galerkin (DG) method is the subject of much current research toward this goal. The spectral difference (SD) method has recently emerged as a p...

A.H. BHRAWY1,2, A.A. AL-ZAHRANI3, Y.A. ALHAMED3, D. BALEANU3,4,5 1Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia E-mail: [email protected] 2Department of Mathematics, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt 3Department of Chemical and Materials Engineering, Faculty of Engineering, King Abdulaziz University, P.O. Box 80204, J...

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...

in this paper, we consider the second-kind chebyshev polynomials (skcps) for the numerical solution of the fractional optimal control problems (focps). firstly, an introduction of the fractional calculus and properties of the shifted skcps are given and then operational matrix of fractional integration is introduced. next, these properties are used together with the legendre-gauss quadrature fo...