{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T22:38:01Z","timestamp":1776724681706,"version":"3.51.2"},"reference-count":10,"publisher":"American Mathematical Society (AMS)","issue":"223","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper we discuss the collocation method for a large class of Fredholm linear integro-differential equations. It will be shown that, when a certain higher order interpolation operation is added to the collocation solution of this equation, the new approximations will, under suitable assumptions, admit a multiterm error expansion in even powers of the step-size\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h\">\n                        <mml:semantics>\n                          <mml:mi>h<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">h<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    . Based on this expansion, ideal multilevel correction results of this collocation solution are obtained.\n                  <\/p>","DOI":"10.1090\/s0025-5718-98-00956-9","type":"journal-article","created":{"date-parts":[[2002,7,26]],"date-time":"2002-07-26T18:14:44Z","timestamp":1027707284000},"page":"987-999","source":"Crossref","is-referenced-by-count":18,"title":["Interpolation correction for collocation solutions of Fredholm integro-differential equations"],"prefix":"10.1090","volume":"67","author":[{"given":"Qiya","family":"Hu","sequence":"first","affiliation":[]}],"member":"14","published-online":{"date-parts":[[1998]]},"reference":[{"key":"1","doi-asserted-by":"publisher","first-page":"582","DOI":"10.1137\/0710052","article-title":"Collocation at Gaussian points","volume":"10","author":"de Boor, Carl","year":"1973","journal-title":"SIAM J. Numer. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0036-1429","issn-type":"print"},{"key":"2","unstructured":"J. Lei and X. Huang, The projection methods for operator equations, Wuhan University Press 1987."},{"key":"3","isbn-type":"print","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511569609","volume-title":"Computational methods for integral equations","author":"Delves, L. M.","year":"1985","ISBN":"https:\/\/id.crossref.org\/isbn\/0521266297"},{"issue":"2","key":"4","first-page":"28","article-title":"Extrapolation of finite element solutions to a class of integro-differential equations","volume":"14","author":"Hu, Qi Ya","year":"1992","journal-title":"Natur. Sci. J. Xiangtan Univ.","ISSN":"https:\/\/id.crossref.org\/issn\/1000-5900","issn-type":"print"},{"key":"5","unstructured":"Q. Hu, Extrapolation for collocation solutions of Volterra integro-differential equations, Chinese J. Numer. Math. Appl. 18(1996), No.2, 28-37."},{"key":"6","unstructured":"Q. Hu, Acceleration of Convergence for Galerkin method solutions to Fredholm Integro-differential Equations, Syst. Sci. and Math. 17(1997), 14-18."},{"issue":"1","key":"7","first-page":"171","article-title":"The numerical solution of linear integro-differential equations by projection methods","volume":"9","author":"Volk, Wolfgang","year":"1985","journal-title":"J. Integral Equations","ISSN":"https:\/\/id.crossref.org\/issn\/0163-5549","issn-type":"print"},{"issue":"1","key":"8","doi-asserted-by":"publisher","first-page":"63","DOI":"10.1016\/0377-0427(88)90388-3","article-title":"The iterated Galerkin method for linear integro-differential equations","volume":"21","author":"Volk, Wolfgang","year":"1988","journal-title":"J. Comput. Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0377-0427","issn-type":"print"},{"issue":"3","key":"9","first-page":"278","article-title":"An extrapolation method for finite element approximation of integro-differential equations with parameters","volume":"3","author":"Zhou, Ai Hui","year":"1990","journal-title":"Systems Sci. Math. Sci.","ISSN":"https:\/\/id.crossref.org\/issn\/1000-9590","issn-type":"print"},{"issue":"2","key":"10","first-page":"1","article-title":"Multilevel correction for the finite element method and the boundary element method","volume":"14","author":"Zhu, Qi Ding","year":"1992","journal-title":"Natur. Sci. J. Xiangtan Univ.","ISSN":"https:\/\/id.crossref.org\/issn\/1000-5900","issn-type":"print"}],"container-title":["Mathematics of Computation"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/www.ams.org\/mcom\/1998-67-223\/S0025-5718-98-00956-9\/S0025-5718-98-00956-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"},{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-223\/S0025-5718-98-00956-9\/S0025-5718-98-00956-9.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T21:47:48Z","timestamp":1776721668000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/mcom\/1998-67-223\/S0025-5718-98-00956-9\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1998]]},"references-count":10,"journal-issue":{"issue":"223","published-print":{"date-parts":[[1998,7]]}},"alternative-id":["S0025-5718-98-00956-9"],"URL":"https:\/\/doi.org\/10.1090\/s0025-5718-98-00956-9","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6842","0025-5718"],"issn-type":[{"value":"1088-6842","type":"electronic"},{"value":"0025-5718","type":"print"}],"subject":[],"published":{"date-parts":[[1998]]}}}