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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An extrapolation method for a class of boundary integral equations


Authors: Yuesheng Xu and Yunhe Zhao
Journal: Math. Comp. 65 (1996), 587-610
MSC (1991): Primary 65R20, 65B05, 45L10
MathSciNet review: 1333328
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Abstract: Boundary value problems of the third kind are converted into boundary integral equations of the second kind with periodic logarithmic kernels by using Green's formulas. For solving the induced boundary integral equations, a Nyström scheme and its extrapolation method are derived for periodic Fredholm integral equations of the second kind with logarithmic singularity. Asymptotic expansions for the approximate solutions obtained by the Nyström scheme are developed to analyze the extrapolation method. Some computational aspects of the methods are considered, and two numerical examples are given to illustrate the acceleration of convergence.


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Additional Information

Yuesheng Xu
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
Email: xu@plains.Nodak.edu

Yunhe Zhao
Affiliation: Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105
Email: yunhe@plains.Nodak.edu

DOI: http://dx.doi.org/10.1090/S0025-5718-96-00723-5
PII: S 0025-5718(96)00723-5
Keywords: Boundary value problem, boundary integral equations, Euler-Maclaurin formula, extrapolation scheme, Nystr\"om method, periodic logarithmic Fredholm integral equations, asymptotic expansion
Received by editor(s): February 21, 1994
Received by editor(s) in revised form: October 4, 1994
Additional Notes: This work is partially supported by NASA under grant NAG 3-1312
Article copyright: © Copyright 1996 American Mathematical Society



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