{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:49:58Z","timestamp":1776721798594,"version":"3.51.2"},"reference-count":14,"publisher":"American Mathematical Society (AMS)","issue":"214","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>Boundary value problems of the third kind are converted into boundary integral equations of the second kind with periodic logarithmic kernels by using Green\u2019s formulas. For solving the induced boundary integral equations, a Nystr\u00f6m 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 Nystr\u00f6m 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.<\/p>","DOI":"10.1090\/s0025-5718-96-00723-5","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"587-610","source":"Crossref","is-referenced-by-count":20,"title":["An extrapolation method for a class of boundary integral equations"],"prefix":"10.1090","volume":"65","author":[{"given":"Yuesheng","family":"Xu","sequence":"first","affiliation":[]},{"given":"Yunhe","family":"Zhao","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1996]]},"reference":[{"key":"1","series-title":"Prentice-Hall Series in Automatic Computation","volume-title":"Collectively compact operator approximation theory and applications to integral equations","author":"Anselone, Philip M.","year":"1971"},{"key":"2","doi-asserted-by":"publisher","first-page":"248","DOI":"10.1007\/BF01404695","article-title":"The numerical solution of Fredholm integral equations of the second kind with singular kernels","volume":"19","author":"Atkinson, Kendall","year":"1972","journal-title":"Numer. 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Math. and Phys.","ISSN":"https:\/\/id.crossref.org\/issn\/0097-1421","issn-type":"print"},{"key":"9","doi-asserted-by":"crossref","unstructured":"L. Navot, A further extension of the Euler-Maclaurin summation formula, J. Math. and Phys. 41 (1962), 155-163.","DOI":"10.1002\/sapm1962411155"},{"issue":"3","key":"10","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1007\/BF01404466","article-title":"On the boundary element method for some nonlinear boundary value problems","volume":"53","author":"Ruotsalainen, K.","year":"1988","journal-title":"Numer. 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