A modified algorithm for the Clenshaw-Curtis method

Abstract

In this paper, we introduce a modified algorithm for the Clenshaw-Curtis (CC) quadrature formula. The coefficients of the formula are approximated by using a finite linear combination of Legendre polynomials in the Least Squares sense to make the CC method well disposed for numerical solution of the definite integral.

We design and analyze the modified CC algorithm. Numerical examples are given to demonstrate the efficiency and the accuracy of the proposed algorithm. The obtained results show that the proposed algorithm perform better and much more efficient than the classical Clenshaw-Curtis method.

Keywords:

• Clenshaw-Curtis method
• Legendre polynomials
• Least Squares