Faculty Advisor or Committee Member

Professor Mayer Humi, Advisor

Identifier

etd-042413-133119

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.

Publisher

Worcester Polytechnic Institute

Degree Name

MS

Department

Mathematical Sciences

Project Type

Thesis

Date Accepted

2013-04-24

Accessibility

Unrestricted

Subjects

Chebyshev Polynomials, Quadrature, Clenshaw-Curtis

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