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The problems considered may be modeled either by ordinary differential equations (state space description) or by differential algebraic equations (descriptor form). A SHAKE-SHAKE and a RATTLE-SHAKE algorithm are presented, but higher-order versions exist.<\/jats:p>","DOI":"10.1137\/080738556","type":"journal-article","created":{"date-parts":[[2010,7,8]],"date-time":"2010-07-08T18:04:19Z","timestamp":1278612259000},"page":"2029-2046","source":"Crossref","is-referenced-by-count":20,"title":["Heterogeneous Multiscale Methods for Mechanical Systems with Vibrations"],"prefix":"10.1137","volume":"32","author":[{"given":"M. P.","family":"Calvo","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"J. 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