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Mathematics of Computation

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Nyström-Clenshaw-Curtis quadrature for integral equations with discontinuous kernels


Authors: Sheon-Young Kang, Israel Koltracht and George Rawitscher
Journal: Math. Comp. 72 (2003), 729-756
MSC (2000): Primary 45B05, 45J05, 65Rxx, 65R20, 81U10
DOI: https://doi.org/10.1090/S0025-5718-02-01431-X
Published electronically: March 8, 2002
MathSciNet review: 1954965
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Abstract: A new highly accurate numerical approximation scheme based on a Gauss type Clenshaw-Curtis quadrature for Fredholm integral equations of the second kind

\begin{displaymath}x(t)+\int^{b}_{a}k(t,s)x(s)ds=y(t),\end{displaymath}

whose kernel $k(t,s)$ is either discontinuous or not smooth along the main diagonal, is presented. This scheme is of spectral accuracy when $k(t,s)$ is infinitely differentiable away from the diagonal $ t = s$. Relation to the singular value decomposition is indicated. Application to integro-differential Schrödinger equations with nonlocal potentials is given.


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Additional Information

Sheon-Young Kang
Affiliation: Department of Mathematics, Purdue University North Central, Westville, Indiana 46391
Email: skang@purduenc.edu

Israel Koltracht
Affiliation: Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269
Email: kolt@math.uconn.edu

George Rawitscher
Affiliation: Department of Physics, University of Connecticut, Storrs, Connecticut 06269
Email: rawitsch@uconnvm.uconn.edu

DOI: https://doi.org/10.1090/S0025-5718-02-01431-X
Keywords: Discontinuous kernels, fast algorithms, nonlocal potentials
Received by editor(s): March 29, 2001
Received by editor(s) in revised form: July 9, 2001
Published electronically: March 8, 2002
Additional Notes: The work of the first author is partially supported by a fellowship from alumni of Mathematics Department, Chungnam National University, Korea.
Article copyright: © Copyright 2002 American Mathematical Society