{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T18:21:31Z","timestamp":1776795691835,"version":"3.51.2"},"reference-count":36,"publisher":"American Mathematical Society (AMS)","issue":"282","license":[{"start":{"date-parts":[[2013,9,10]],"date-time":"2013-09-10T00:00:00Z","timestamp":1378771200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Math. Comp."],"abstract":"<p>\n                    We analyze the convergence behavior of collocation schemes applied to approximate solutions of BVPs in nonlinear index 1 DAEs, which exhibit a critical point at the left boundary. Such a critical point of the DAE causes a singularity in the inherent nonlinear ODE system. In particular, we focus on the case when the inherent ODE system is singular with a\n                    <italic>singularity of the first kind<\/italic>\n                    and apply polynomial collocation to the\n                    <italic>original DAE system<\/italic>\n                    . We show that for a certain class of well-posed boundary value problems in DAEs having a sufficiently smooth solution, the global error of the collocation scheme converges uniformly with the so-called stage order. Due to the singularity, superconvergence at the mesh points does not hold in general. The theoretical results are supported by numerical experiments.\n                  <\/p>","DOI":"10.1090\/s0025-5718-2012-02637-8","type":"journal-article","created":{"date-parts":[[2012,9,10]],"date-time":"2012-09-10T09:14:48Z","timestamp":1347268488000},"page":"893-918","source":"Crossref","is-referenced-by-count":3,"title":["Convergence of collocation schemes for boundary value problems in nonlinear index 1 DAEs with a singular point"],"prefix":"10.1090","volume":"82","author":[{"given":"Alexander","family":"Dick","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Othmar","family":"Koch","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Roswitha","family":"M\u00e4rz","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ewa","family":"Weinm\u00fcller","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"14","published-online":{"date-parts":[[2012,9,10]]},"reference":[{"key":"1","unstructured":"P. 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