Worcester Polytechnic Institute Electronic Theses and Dissertations Collection

Title page for ETD etd-042413-133119


Document Typemasters report
Author NameBarden, Jeffrey M.
URNetd-042413-133119
TitleA Modified Clenshaw-Curtis Quadrature Algorithm
DegreeMS
DepartmentMathematical Sciences
Advisors
  • Professor Mayer Humi, Advisor
  • Keywords
  • Chebyshev Polynomials
  • Quadrature
  • Clenshaw-Curtis
  • Date of Presentation/Defense2013-04-24
    Availability unrestricted

    Abstract

    This project presents a modified method of numerical integration for a “well behaved” function over the finite interval [-1,1]. Similar to the Clenshaw-Curtis quadrature rule, this new algorithm relies on expressing the integrand as an expansion of Chebyshev polynomials of the second kind. The truncated series is integrated term-by-term yielding an approximation for the integral of which we wish to compute. The modified method is then contrasted with its predecessor Clenshaw-Curtis, as well as the classical method of Gauss-Legendre in terms of convergence behavior, error analysis and computational efficiency. Lastly, illustrative examples are shown which demonstrate the dependence that the convergence has on the given function to be integrated.

    Files
  • A_Modified_Clenshaw-Curtis_Quadrature_Algorithm.pdf

  • Browse by Author | Browse by Department | Search all available ETDs

    [WPI] [Library] [Home] [Top]

    Questions? Email etd-questions@wpi.edu
    Maintained by webmaster@wpi.edu