{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,3]],"date-time":"2026-06-03T19:06:47Z","timestamp":1780513607373,"version":"3.54.1"},"reference-count":32,"publisher":"American Mathematical Society (AMS)","issue":"298","license":[{"start":{"date-parts":[[2016,9,2]],"date-time":"2016-09-02T00:00:00Z","timestamp":1472774400000},"content-version":"am","delay-in-days":366,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    In this paper, we propose a multistep Legendre-Gauss spectral collocation method for nonlinear second-kind Volterra integral equations (VIEs) with vanishing variable delays. This method is easy to implement and possesses high-order accuracy. We also provide a rigorous convergence analysis of the\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"h p\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:mi>h<\/mml:mi>\n                            <mml:mi>p<\/mml:mi>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">hp<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -version of the multistep spectral collocation method under\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"upper L squared\">\n                        <mml:semantics>\n                          <mml:msup>\n                            <mml:mi>L<\/mml:mi>\n                            <mml:mn>2<\/mml:mn>\n                          <\/mml:msup>\n                          <mml:annotation encoding=\"application\/x-tex\">L^2<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    -norm. Numerical results confirm the theoretical predictions.\n                  <\/p>","DOI":"10.1090\/mcom\/3023","type":"journal-article","created":{"date-parts":[[2015,9,2]],"date-time":"2015-09-02T08:42:43Z","timestamp":1441183363000},"page":"635-666","source":"Crossref","is-referenced-by-count":11,"title":["An \u210e\ud835\udc5d-spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays"],"prefix":"10.1090","volume":"85","author":[{"given":"Wang","family":"Zhong-qing","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Sheng","family":"Chang-tao","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"14","published-online":{"date-parts":[[2015,9,2]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"49","DOI":"10.4208\/jcm.1006-m3150","article-title":"Convergence analysis of spectral methods for integro-differential equations with vanishing proportional delays","volume":"29","author":"Ali, Ishtiaq","year":"2011","journal-title":"J. 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