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An extrapolation method for a class of boundary integral equations
Author(s):
Yuesheng
Xu;
Yunhe
Zhao.
Journal:
Math. Comp.
65
(1996),
587-610.
MSC (1991):
Primary 65R20, 65B05, 45L10
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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:
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
Copyright of article:
Copyright
1996,
American Mathematical Society
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