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Although the scheme is formally second order, the most intensive computations (the close-approach dynamics) are executed at higher order, thus improving the overall accuracy. Numerical experiments indicate that the method can effectively treat few-body gravitational problems with two-body close approaches, and it compares favorably with other schemes presented in the literature.<\/jats:p>","DOI":"10.1137\/s1064827599355566","type":"journal-article","created":{"date-parts":[[2003,6,11]],"date-time":"2003-06-11T11:12:06Z","timestamp":1055329926000},"page":"1016-1035","source":"Crossref","is-referenced-by-count":12,"title":["A Time-Reversible, Regularized, Switching Integrator for the\n                    <i>N<\/i>\n                    -Body Problem"],"prefix":"10.1137","volume":"22","author":[{"given":"Anne","family":"Kvaerno","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ben","family":"Leimkuhler","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2006,7,25]]},"reference":[{"key":"R1","unstructured":"Sverre Aarseth, Direct methods for N\u2010body simulations, Lecture Notes in Phys., Vol. 433, Springer, Berlin, 1994, 277\u20133121296491"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019127111709"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1098\/rsta.1999.0360"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/0914057"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1046\/j.1365-8711.1999.02379.x"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1093\/imanum\/7.1.1"},{"key":"R7","doi-asserted-by":"publisher","DOI":"10.1086\/300541"},{"key":"R8","unstructured":"H. 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