{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,15]],"date-time":"2026-07-15T17:29:25Z","timestamp":1784136565920,"version":"3.55.0"},"reference-count":33,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2015,4,1]],"date-time":"2015-04-01T00:00:00Z","timestamp":1427846400000},"content-version":"unspecified","delay-in-days":90,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["LMS J. Comput. Math."],"published-print":{"date-parts":[[2015]]},"abstract":"<jats:p>Our main purpose in this paper is to propose the piecewise Legendre spectral-collocation method to solve Volterra integro-differential equations. We provide convergence analysis to show that the numerical errors in our method decay in<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"gif\" xlink:type=\"simple\" xlink:href=\"S1461157014000485_inline1\"\/><jats:tex-math>$h^{m}N^{-m}$<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>-version rate. These results are better than the piecewise polynomial collocation method and the global Legendre spectral-collocation method. The provided numerical examples confirm these theoretical results.<\/jats:p>","DOI":"10.1112\/s1461157014000485","type":"journal-article","created":{"date-parts":[[2015,4,8]],"date-time":"2015-04-08T10:37:27Z","timestamp":1428489447000},"page":"231-249","source":"Crossref","is-referenced-by-count":12,"title":["Piecewise Legendre spectral-collocation method for Volterra integro-differential equations"],"prefix":"10.1112","volume":"18","author":[{"given":"Zhendong","family":"Gu","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yanping","family":"Chen","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"311","published-online":{"date-parts":[[2015,4,1]]},"reference":[{"key":"S1461157014000485_r28","doi-asserted-by":"crossref","first-page":"419","DOI":"10.4208\/nmtma.2011.m1028","article-title":"Convergence analysis of the Legendre spectral collocation methods for second order Volterra integro-differential equations","volume":"4","author":"Wei","year":"2011","journal-title":"Numer. 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