{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T17:26:08Z","timestamp":1787333168521,"version":"build-2736575974"},"reference-count":59,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","funder":[{"DOI":"10.13039\/100000893","name":"Simons Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000893","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2024,2,29]]},"abstract":"<jats:p>Abstract.<\/jats:p>\n                  <jats:p>We introduce an efficient numerical method for second-order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory phase function that obeys the nonlinear Riccati equation. We propose a defect correction iteration that gives an asymptotic series for such a phase function; this is numerically approximated on a Chebyshev grid with a small number of nodes. For analytic coefficients we prove that each iteration, up to a certain maximum number, reduces the residual by a factor of order of the local frequency. The algorithm adapts both the stepsize and the choice of method, switching to a conventional spectral collocation method away from oscillatory regions. In numerical experiments we find that our proposal outperforms other state-of-the-art oscillatory solvers, most significantly at low to intermediate frequencies and at low tolerances, where it may use up to [Formula: see text] times fewer function evaluations. Even in high-frequency regimes, our implementation is on average 10 times faster than other specialized solvers.<\/jats:p>","DOI":"10.1137\/23m1546609","type":"journal-article","created":{"date-parts":[[2024,1,29]],"date-time":"2024-01-29T04:46:50Z","timestamp":1706503610000},"page":"295-321","source":"Crossref","is-referenced-by-count":5,"title":["An Adaptive Spectral Method for Oscillatory Second-Order Linear ODEs with Frequency-Independent Cost"],"prefix":"10.1137","volume":"62","author":[{"given":"Fruzsina J.","family":"Agocs","sequence":"first","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alex H.","family":"Barnett","sequence":"additional","affiliation":[{"name":"Center for Computational Mathematics, Flatiron Institute, Simons Foundation, New York, NY 10010 USA."}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2024,1,29]]},"reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevA.38.1679"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.21105\/joss.02830"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.21105\/joss.05430"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevResearch.2.013030"},{"key":"ref5","unstructured":"F. 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