Document Type masters report Author Name Barden, Jeffrey M. URN etd-042413-133119 Title A Modified Clenshaw-Curtis Quadrature Algorithm Degree MS Department Mathematical Sciences Advisors Professor Mayer Humi, Advisor Keywords Chebyshev Polynomials Quadrature Clenshaw-Curtis Date of Presentation/Defense 2013-04-24 Availability unrestricted
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.
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