This project presents a modified method of numerical integration for a â€œwell behavedâ€� 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.
Worcester Polytechnic Institute
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Barden, Jeffrey M., "A Modified Clenshaw-Curtis Quadrature Algorithm" (2013). Masters Theses (All Theses, All Years). 265.
Chebyshev Polynomials, Quadrature, Clenshaw-Curtis