{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,2]],"date-time":"2026-06-02T02:52:30Z","timestamp":1780368750772,"version":"3.54.1"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2007,12,21]],"date-time":"2007-12-21T00:00:00Z","timestamp":1198195200000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Numer. Math."],"published-print":{"date-parts":[[2008,3]]},"DOI":"10.1007\/s00211-007-0125-7","type":"journal-article","created":{"date-parts":[[2007,12,20]],"date-time":"2007-12-20T11:47:21Z","timestamp":1198151241000},"page":"143-165","source":"Crossref","is-referenced-by-count":57,"title":["The superconvergence of Newton\u2013Cotes rules for the Hadamard finite-part integral on an interval"],"prefix":"10.1007","volume":"109","author":[{"given":"Jiming","family":"Wu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Weiwei","family":"Sun","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2007,12,21]]},"reference":[{"key":"125_CR1","volume-title":"Special Functions of Mathematics for Engineers","author":"L.C. Andrews","year":"1992","unstructured":"Andrews, L.C.: Special Functions of Mathematics for Engineers, 2nd edn. McGraw-Hill, Inc., New York (1992)","edition":"2"},{"key":"125_CR2","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s002110000134","volume":"85","author":"M. Ainsworth","year":"2000","unstructured":"Ainsworth, M., Guo, B.: An additive Schwarz preconditioner for p-version boundary element approximation of the hypersingular operator in three dimensions. Numer. Math. 85, 343\u2013366 (2000)","journal-title":"Numer. Math."},{"key":"125_CR3","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1137\/S1064827503428539","volume":"27","author":"G. Bao","year":"2005","unstructured":"Bao, G., Sun, W.: A fast algorithm for the electromagnetic scattering from a large cavity. SIAM J. Sci. Comput. 27, 553\u2013574 (2005)","journal-title":"SIAM J. Sci. Comput."},{"key":"125_CR4","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511543234","volume-title":"Collocation Methods for Volterra Integral and Related Functional Equations","author":"H. Brunner","year":"2004","unstructured":"Brunner, H.: Collocation Methods for Volterra Integral and Related Functional Equations. Cambridge University Press, UK (2004)"},{"key":"125_CR5","doi-asserted-by":"crossref","first-page":"496","DOI":"10.1002\/nme.1077","volume":"61","author":"U.J. Choi","year":"2004","unstructured":"Choi, U.J., Kim, S.W., Yun, B.I.: Improvement of the asymptotic behaviour of the Euler\u2013Maclaurin formula for Cauchy principal value and Hadamard finite-part integrals. Int. J. Numer. Methods Eng. 61, 496\u2013513 (2004)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"125_CR6","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1002\/nme.218","volume":"51","author":"Q.K. Du","year":"2001","unstructured":"Du, Q.K.: Evaluations of certain hypersingular integrals on interval. Int. J. Numer. Methods Eng. 51, 1195\u20131210 (2001)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"125_CR7","doi-asserted-by":"crossref","first-page":"453","DOI":"10.1007\/s002110050295","volume":"77","author":"D. Elliott","year":"1997","unstructured":"Elliott, D., Venturino, E.: Sigmoidal transformations and the Euler\u2013Maclaurin expansion for evaluating certain Hadamard finite-part integrals. Numer. Math. 77, 453\u2013465 (1997)","journal-title":"Numer. Math."},{"key":"125_CR8","unstructured":"Fairweather G., Ma, H., Sun, W.: Orthogonal spline collocation methods for the Navier\u2013Stokes equations in stream function and vorticity formulation. Numer. Methods PDEs (in press)"},{"key":"125_CR9","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1016\/j.cam.2003.08.059","volume":"163","author":"T. Hasegawa","year":"2004","unstructured":"Hasegawa, T.: Uniform approximations to finite Hilbert transform and its derivative. J. Comput. Appl. Math. 163, 127\u2013138 (2004)","journal-title":"J. Comput. Appl. Math."},{"key":"125_CR10","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1002\/(SICI)1097-0207(19990120)44:2<205::AID-NME499>3.0.CO;2-8","volume":"44","author":"C.Y. Hui","year":"1999","unstructured":"Hui, C.Y., Shia, D.: Evaluations of hypersingular integrals using Gaussian quadrature. Int. J. Numer. Methods Eng. 44, 205\u2013214 (1999)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"125_CR11","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1090\/S0025-5718-1985-0771040-8","volume":"44","author":"N.I. Ioakimidis","year":"1985","unstructured":"Ioakimidis, N.I.: On the uniform convergence of Gaussian quadrature rules for Cauchy principal value integrals and their derivatives. Math. Comp. 44, 191\u2013198 (1985)","journal-title":"Math. Comp."},{"key":"125_CR12","doi-asserted-by":"crossref","first-page":"469","DOI":"10.1002\/nme.582","volume":"56","author":"P. Kim","year":"2003","unstructured":"Kim, P., Jin, U.C.: Two trigonometric quadrature formulae for evaluating hypersingular integrals. Inter. J. Numer. Methods Eng. 56, 469\u2013486 (2003)","journal-title":"Inter. J. Numer. Methods Eng."},{"key":"125_CR13","doi-asserted-by":"crossref","first-page":"345","DOI":"10.1007\/BF02240199","volume":"35","author":"P. Linz","year":"1985","unstructured":"Linz, P.: On the approximate computation of certain strongly singular integrals. Computing 35, 345\u2013353 (1985)","journal-title":"Computing"},{"key":"125_CR14","first-page":"16","volume":"4","author":"S. Mao","year":"2007","unstructured":"Mao, S., Chen, S., Shi, D.: Convergence and superconvergence of a nonconforming finite element on anisotropic meshes. Int. J. Numer. Anal. Model. 4, 16\u201338 (2007)","journal-title":"Int. J. Numer. Anal. Model."},{"key":"125_CR15","doi-asserted-by":"crossref","first-page":"9","DOI":"10.1016\/0377-0427(94)90287-9","volume":"50","author":"G. Monegato","year":"1994","unstructured":"Monegato, G.: Numerical evaluation of hypersingular integrals. J. Comput. Appl. Math. 50, 9\u201331 (1994)","journal-title":"J. Comput. Appl. Math."},{"key":"125_CR16","unstructured":"Monegato, G.: Definitions, properties and applications of finite part integrals, submitted"},{"key":"125_CR17","doi-asserted-by":"crossref","first-page":"447","DOI":"10.1007\/BF01395957","volume":"36","author":"D.F. Paget","year":"1980\/81","unstructured":"Paget, D.F.: The numerical evaluation of Hadamard finite-part integrals. Numer. Math. 36, 447\u2013453 (1980\/81)","journal-title":"Numer. Math."},{"key":"125_CR18","doi-asserted-by":"crossref","first-page":"1962","DOI":"10.1137\/S0036142997322722","volume":"36","author":"W. Sun","year":"1999","unstructured":"Sun, W.: The spectral analysis of Hermite cubic spline collocation systems. SIAM J. Numer. Anal. 36, 1962\u20131975 (1999)","journal-title":"SIAM J. Numer. Anal."},{"key":"125_CR19","doi-asserted-by":"crossref","first-page":"297","DOI":"10.1007\/s00607-005-0131-5","volume":"75","author":"W. Sun","year":"2005","unstructured":"Sun, W., Wu, J.M.: Newton\u2013Cotes formulae for the numerical evaluation of certain hypersingular integral. Computing 75, 297\u2013309 (2005)","journal-title":"Computing"},{"key":"125_CR20","doi-asserted-by":"crossref","unstructured":"Sun, W., Wu, J.M.: Interpolatory quadrature rules for Hadamard finite-part integrals and their supperconvergence. IMA J. Numer. Anal. (2007) (accepted)","DOI":"10.1093\/imanum\/drm037"},{"key":"125_CR21","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1016\/0045-7949(90)90215-N","volume":"36","author":"W. Sun","year":"1990","unstructured":"Sun, W., Zamani, N.G.: Adaptive mesh redistribution for the boundary element method in elastostatics. Comput. Struct. 36, 1081\u20131088 (1990)","journal-title":"Comput. Struct."},{"key":"125_CR22","doi-asserted-by":"crossref","first-page":"13","DOI":"10.1002\/nme.1620300103","volume":"30","author":"G. Tsamasphyros","year":"1990","unstructured":"Tsamasphyros, G., Dimou, G.: Gauss quadrature rules for finite part integrals. Int. J. Numer. Methods Eng. 30, 13\u201326 (1990)","journal-title":"Int. J. Numer. Methods Eng."},{"key":"125_CR23","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1093\/imanum\/drh025","volume":"25","author":"J.M. Wu","year":"2005","unstructured":"Wu, J.M., L\u00fc, Y.: A superconvergence result for the second-order Newton\u2013Cotes formula for certain finite-part integrals. IMA J. Numer. Anal. 25, 253\u2013263 (2005)","journal-title":"IMA J. Numer. Anal."},{"key":"125_CR24","unstructured":"Wu, J.M., Wang, Y., Li, W., Sun, W.: Toeplitz-type approximations to the Hadamard integral operators and their applications in electromagnetic cavity problems. Appl. Numer. Math. (2007) (online)"},{"key":"125_CR25","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1007\/s00211-005-0647-9","volume":"102","author":"J.M. Wu","year":"2005","unstructured":"Wu, J.M., Sun, W.: The superconvergence of the composite trapezoidal rule for Hadamard finite part integrals. Numer. Math. 102, 343\u2013363 (2005)","journal-title":"Numer. Math."}],"container-title":["Numerische Mathematik"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0125-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00211-007-0125-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00211-007-0125-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,23]],"date-time":"2019-05-23T16:22:40Z","timestamp":1558628560000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00211-007-0125-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,12,21]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2008,3]]}},"alternative-id":["125"],"URL":"https:\/\/doi.org\/10.1007\/s00211-007-0125-7","relation":{},"ISSN":["0029-599X","0945-3245"],"issn-type":[{"value":"0029-599X","type":"print"},{"value":"0945-3245","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,12,21]]}}}