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

DOI:
https://doi.org/10.1090/S0025-5718-96-00723-5

MathSciNet review:
1333328

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0025-5718-96-00723-5

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