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Chebfun and numerical quadrature

Science China Mathematics volume 55, pages 1749–1760 (2012)Cite this article

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.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, Oxford, OX1 3LB, UK

    Nicholas Hale & Lloyd N. Trefethen

Authors
  1. Nicholas Hale
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  2. Lloyd N. Trefethen
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Correspondence to Lloyd N. Trefethen.

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Hale, N., Trefethen, L.N. Chebfun and numerical quadrature. Sci. China Math. 55, 1749–1760 (2012). https://doi.org/10.1007/s11425-012-4474-z

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  • DOI: https://doi.org/10.1007/s11425-012-4474-z

Keywords

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

MSC(2010)

  • 41A55
  • 97N80