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Automatic differentiation enables accurate computation of high-order derivatives of functions without the truncation errors inherent in finite difference calculations. We embed the algorithms in a continuation framework and extend them to compute saddle-node bifurcations of periodic orbits directly. We present data from numerical studies of four test problems, making some comparisons with other methods for computing periodic orbits. These results demonstrate that high-order methods based uponautomatic differentiation are capable of high precision with small meshes.<\/jats:p>","DOI":"10.1137\/s1064827599359278","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"951-985","source":"Crossref","is-referenced-by-count":71,"title":["Computing Periodic Orbits and their Bifurcations with Automatic Differentiation"],"prefix":"10.1137","volume":"22","author":[{"given":"John","family":"Guckenheimer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian","family":"Meloon","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1090\/S0002-9947-1978-0478138-5"},{"key":"R2","unstructured":"U. Ascher, R. Mattheij, and R. 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