{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T13:13:26Z","timestamp":1753881206720,"version":"3.41.2"},"reference-count":12,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,11,12]],"date-time":"2012-11-12T00:00:00Z","timestamp":1352678400000},"content-version":"vor","delay-in-days":316,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11101130","12511414","11551363"],"award-info":[{"award-number":["11101130","12511414","11551363"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003851","name":"Heilongjiang Provincial Education Department","doi-asserted-by":"crossref","award":["11101130","12511414","11551363"],"award-info":[{"award-number":["11101130","12511414","11551363"]}],"id":[{"id":"10.13039\/501100003851","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100003851","name":"Heilongjiang Provincial Education Department","doi-asserted-by":"crossref","award":["11101130","12511414","11551363"],"award-info":[{"award-number":["11101130","12511414","11551363"]}],"id":[{"id":"10.13039\/501100003851","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for <jats:italic>u<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>t<\/jats:italic>) = <jats:italic>a<\/jats:italic><jats:italic>u<\/jats:italic>(<jats:italic>t<\/jats:italic>) + <jats:italic>b<\/jats:italic><jats:italic>u<\/jats:italic>([<jats:italic>t<\/jats:italic>]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.<\/jats:p>","DOI":"10.1155\/2012\/125926","type":"journal-article","created":{"date-parts":[[2012,11,13]],"date-time":"2012-11-13T10:05:56Z","timestamp":1352801156000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Convergence and Stability in Collocation Methods of Equation <i>u<\/i><sup>\u2032<\/sup>(<i>t<\/i>) = <i>a<\/i><i>u<\/i>(<i>t<\/i>) + <i>b<\/i><i>u<\/i>([<i>t<\/i>])"],"prefix":"10.1155","volume":"2012","author":[{"given":"Han","family":"Yan","sequence":"first","affiliation":[]},{"given":"Shufang","family":"Ma","sequence":"additional","affiliation":[]},{"given":"Yanbin","family":"Liu","sequence":"additional","affiliation":[]},{"given":"Hongquan","family":"Sun","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,11,12]]},"reference":[{"key":"e_1_2_9_1_2","first-page":"547","volume-title":"Trends in the Theory and Practice of Nonlinear Differential Equations","author":"Wiener J.","year":"1983"},{"key":"e_1_2_9_2_2","first-page":"571","volume-title":"Differential Equations","author":"Wiener J.","year":"1984"},{"key":"e_1_2_9_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0022-247X(84)90248-8"},{"key":"e_1_2_9_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/S0161171283000599"},{"key":"e_1_2_9_5_2","doi-asserted-by":"crossref","DOI":"10.1142\/1860","volume-title":"Generalized Solutions of Differential Equations","author":"Wiener J.","year":"1993"},{"key":"e_1_2_9_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2003.04.002"},{"key":"e_1_2_9_7_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2003.12.081"},{"key":"e_1_2_9_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2011.05.042"},{"key":"e_1_2_9_9_2","first-page":"251","article-title":"Representation of the solution for linear system of delay equations with distributed parameters","volume":"12","author":"Diblik J.","year":"2012","journal-title":"Nonlinear Dynamics and Systems Theory"},{"key":"e_1_2_9_10_2","first-page":"283","article-title":"On nonlinear abstract neutral differential equations with deviated argument","volume":"10","author":"Pandey D. 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