Science China Mathematics

, Volume 55, Issue 9, pp 1749–1760

Chebfun and numerical quadrature

Articles

DOI: 10.1007/s11425-012-4474-z

Cite this article as:
Hale, N. & Trefethen, L.N. Sci. China Math. (2012) 55: 1749. doi:10.1007/s11425-012-4474-z

Abstract

Chebfun is a Matlab-based software system that overloads Matlab’s discrete operations for vectors and matrices to analogous continuous operations for functions and operators. We begin by describing Chebfun’s fast capabilities for Clenshaw-Curtis and also Gauss-Legendre, -Jacobi, -Hermite, and -Laguerre quadrature, based on algorithms of Waldvogel and Glaser, Liu and Rokhlin. Then we consider how such methods can be applied to quadrature problems including 2D integrals over rectangles, fractional derivatives and integrals, functions defined on unbounded intervals, and the fast computation of weights for barycentric interpolation.

Keywords

Chebfun Clenshaw-Curtis quadrature Gauss quadrature barycentric interpolation formula Riemann-Liouville integral fractional calculus 

MSC(2010)

41A55 97N80 

Copyright information

© Science China Press and Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK

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