{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,2]],"date-time":"2026-02-02T19:49:56Z","timestamp":1770061796721,"version":"3.49.0"},"reference-count":14,"publisher":"Walter de Gruyter GmbH","issue":"4","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11671157"],"award-info":[{"award-number":["11671157"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["91430213"],"award-info":[{"award-number":["91430213"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003091","name":"Shandong Province","doi-asserted-by":"publisher","award":["ZR2017MA005"],"award-info":[{"award-number":["ZR2017MA005"]}],"id":[{"id":"10.13039\/501100003091","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2019,10,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>In this work we study the numerical solution to the Volterra integro-differential algebraic equation. Two numerical examples based on the Legendre collocation scheme are designed. It follows from the convergence proof and numerical experiments\nthat the errors of the approximate solution and the errors of the approximate derivative of the solution\ndecay exponentially.<\/jats:p>","DOI":"10.1515\/cmam-2018-0016","type":"journal-article","created":{"date-parts":[[2019,11,27]],"date-time":"2019-11-27T09:03:13Z","timestamp":1574845393000},"page":"833-847","source":"Crossref","is-referenced-by-count":3,"title":["Legendre Collocation Method for Volterra Integro-Differential Algebraic Equation"],"prefix":"10.1515","volume":"19","author":[{"given":"Yunxia","family":"Wei","sequence":"first","affiliation":[{"name":"Zhejiang University of Water Resources and Electric Power , Hangzhou 310018 , P. R. China"}]},{"given":"Yanping","family":"Chen","sequence":"additional","affiliation":[{"name":"School of Mathematical Sciences , South China Normal University , Guangzhou 510631 , P. R. China"}]},{"given":"Yunqing","family":"Huang","sequence":"additional","affiliation":[{"name":"Hunan Key Laboratory for Computation and Simulation in Science and Engineering , School of Mathematics and Computational Science , Xiangtan University , Xiangtan 411105 , P. R. China"}]}],"member":"374","published-online":{"date-parts":[[2018,6,21]]},"reference":[{"key":"2023033110105338110_j_cmam-2018-0016_ref_001_w2aab3b7e1884b1b6b1ab2ab1Aa","unstructured":"I.  Ali, H.  Brunner and T.  Tang,\nA spectral method for pantograph-type delay differential equations and its convergence analysis,\nJ. Comput. Math. 27 (2009), no. 2\u20133, 254\u2013265."},{"key":"2023033110105338110_j_cmam-2018-0016_ref_002_w2aab3b7e1884b1b6b1ab2ab2Aa","doi-asserted-by":"crossref","unstructured":"H.  Brunner,\nVolterra Integral Equations. An Introduction to Theory and Applications,\nCambridge Monogr. Appl. Comput. Math. 30,\nCambridge University Press, Cambridge, 2017.","DOI":"10.1017\/9781316162491"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_003_w2aab3b7e1884b1b6b1ab2ab3Aa","doi-asserted-by":"crossref","unstructured":"C.  Canuto, M. Y.  Hussaini, A.  Quarteroni and T. A.  Zang,\nSpectral Methods. Fundamentals in Single Domains,\nSci. Comput.,\nSpringer, Berlin, 2006.","DOI":"10.1007\/978-3-540-30726-6"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_004_w2aab3b7e1884b1b6b1ab2ab4Aa","doi-asserted-by":"crossref","unstructured":"Y.  Chen and T.  Tang,\nSpectral methods for weakly singular Volterra integral equations with smooth solutions,\nJ. Comput. Appl. Math. 233 (2009), no. 4, 938\u2013950.","DOI":"10.1016\/j.cam.2009.08.057"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_005_w2aab3b7e1884b1b6b1ab2ab5Aa","doi-asserted-by":"crossref","unstructured":"Y.  Chen and T.  Tang,\nConvergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel,\nMath. Comp. 79 (2010), no. 269, 147\u2013167.","DOI":"10.1090\/S0025-5718-09-02269-8"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_006_w2aab3b7e1884b1b6b1ab2ab6Aa","unstructured":"A. I.  Fedotov,\nLebesgue constant estimation in multidimensional Sobolev space,\nLobachevskii J. Math. 14 (2004), 25\u201332."},{"key":"2023033110105338110_j_cmam-2018-0016_ref_007_w2aab3b7e1884b1b6b1ab2ab7Aa","doi-asserted-by":"crossref","unstructured":"M.  Hadizadeh, F.  Ghoreishi and S.  Pishbin,\nJacobi spectral solution for integral algebraic equations of index-2,\nAppl. Numer. Math. 61 (2011), no. 1, 131\u2013148.","DOI":"10.1016\/j.apnum.2010.08.009"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_008_w2aab3b7e1884b1b6b1ab2ab8Aa","doi-asserted-by":"crossref","unstructured":"C.  Huang and Z.  Zhang,\nSpectral collocation methods for differential-algebraic equations with arbitrary index,\nJ. Sci. Comput. 58 (2014), no. 3, 499\u2013516.","DOI":"10.1007\/s10915-013-9755-3"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_009_w2aab3b7e1884b1b6b1ab2ab9Aa","unstructured":"Y.-L.  Jiang,\nWaveform relaxation methods of nonlinear integral-differential-algebraic equations,\nJ. Comput. Math. 23 (2005), no. 1, 49\u201366."},{"key":"2023033110105338110_j_cmam-2018-0016_ref_010_w2aab3b7e1884b1b6b1ab2ac10Aa","doi-asserted-by":"crossref","unstructured":"J.-P.  Kauthen,\nImplicit Runge\u2013Kutta methods for some integrodifferential-algebraic equations,\nAppl. Numer. Math. 13 (1993), no. 1\u20133, 125\u2013134.","DOI":"10.1016\/0168-9274(93)90136-F"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_011_w2aab3b7e1884b1b6b1ab2ac11Aa","unstructured":"J.  Shen and T.  Tang,\nSpectral and High-Order Methods with Applications,\nMath. Monogr. Ser. 3,\nScience Press Beijing, Beijing, 2006."},{"key":"2023033110105338110_j_cmam-2018-0016_ref_012_w2aab3b7e1884b1b6b1ab2ac12Aa","doi-asserted-by":"crossref","unstructured":"Y.  Wei and Y.  Chen,\nLegendre spectral collocation methods for pantograph Volterra delay-integro-differential equations,\nJ. Sci. Comput. 53 (2012), no. 3, 672\u2013688.","DOI":"10.1007\/s10915-012-9595-6"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_013_w2aab3b7e1884b1b6b1ab2ac13Aa","doi-asserted-by":"crossref","unstructured":"Y.  Wei and Y.  Chen,\nLegendre spectral collocation method for neutral and high-order Volterra integro-differential equation,\nAppl. Numer. Math. 81 (2014), 15\u201329.","DOI":"10.1016\/j.apnum.2014.02.012"},{"key":"2023033110105338110_j_cmam-2018-0016_ref_014_w2aab3b7e1884b1b6b1ab2ac14Aa","doi-asserted-by":"crossref","unstructured":"J.  Zhao and S.  Wang,\nJacobi spectral solution for weakly singular integral algebraic equations of index-1,\nAdv. Difference Equ. 2014 (2014), Paper No. 165.","DOI":"10.1186\/1687-1847-2014-165"}],"container-title":["Computational Methods in Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/view\/journals\/cmam\/19\/4\/article-p833.xml","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0016\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0016\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,3,31]],"date-time":"2023-03-31T11:22:53Z","timestamp":1680261773000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/cmam-2018-0016\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2018,6,21]]},"references-count":14,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2018,4,10]]},"published-print":{"date-parts":[[2019,10,1]]}},"alternative-id":["10.1515\/cmam-2018-0016"],"URL":"https:\/\/doi.org\/10.1515\/cmam-2018-0016","relation":{},"ISSN":["1609-9389","1609-4840"],"issn-type":[{"value":"1609-9389","type":"electronic"},{"value":"1609-4840","type":"print"}],"subject":[],"published":{"date-parts":[[2018,6,21]]}}}