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Similar to the way that Runge--Kutta and partitioned Runge--Kutta methods preserve quadratic invariants and symplecticity for Hamiltonian systems, ERK and PERK methods exactly preserve conformal symplecticity, as well as decay (or growth) rates in linear and quadratic invariants, under certain constraints on their coefficient functions. Numerical experiments illustrate the higher-order accuracy and structure-preserving properties of various ERK methods, demonstrating clear advantages over classical conservative Runge--Kutta methods, as well as usefulness for solving a wide range of differential equations.<\/jats:p>","DOI":"10.1137\/16m1071171","type":"journal-article","created":{"date-parts":[[2017,4,13]],"date-time":"2017-04-13T11:28:02Z","timestamp":1492082882000},"page":"A593-A612","source":"Crossref","is-referenced-by-count":36,"title":["Structure-preserving Exponential Runge--Kutta Methods"],"prefix":"10.1137","volume":"39","author":[{"given":"Ashish","family":"Bhatt","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Brian E.","family":"Moore","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2017,4,13]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1137\/040612683"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1007\/s10915-015-0062-z"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/BF01935643"},{"key":"atypb4","doi-asserted-by":"publisher","DOI":"10.1016\/j.cam.2007.05.016"},{"key":"atypb5","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-007-9016-7"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1051\/m2an\/2009020"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1007\/s10543-011-0310-z"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1006\/jcph.2002.6995"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1137\/100811052"},{"key":"atypb10","volume-title":"Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations","author":"Hairer E.","year":"2006"},{"key":"atypb11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1023\/B:ENGI.0000017475.20596.cb","volume":"49","author":"Hartono","journal-title":"J. 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