An extrapolation method for a class of boundary integral equations |
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| Authors: | Yuesheng Xu Yunhe Zhao. |
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| Affiliation: | Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105 ; Department of Mathematics, North Dakota State University, Fargo, North Dakota 58105 |
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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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| Keywords: | Boundary value problem, boundary integral equations, Euler-Maclaurin formula, extrapolation scheme, Nystr" om method, periodic logarithmic Fredholm integral equations, asymptotic expansion |
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