An extrapolation method for a class of boundary integral equations
Authors:
Yuesheng Xu and Yunhe Zhao
Journal:
Math. Comp. 65 (1996), 587610
MSC (1991):
Primary 65R20, 65B05, 45L10
MathSciNet review:
1333328
Fulltext PDF Free Access
Abstract 
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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:
http://dx.doi.org/10.1090/S0025571896007235
PII:
S 00255718(96)007235
Keywords:
Boundary value problem,
boundary integral equations,
EulerMaclaurin 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 31312
Article copyright:
© Copyright 1996
American Mathematical Society
