{"id":"https://openalex.org/W1983702722","doi":"https://doi.org/10.1137/s1064827595282350","title":"A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications","display_name":"A Family of Symplectic Integrators: Stability, Accuracy, and Molecular Dynamics Applications","publication_year":1997,"publication_date":"1997-01-01","ids":{"openalex":"https://openalex.org/W1983702722","doi":"https://doi.org/10.1137/s1064827595282350","mag":"1983702722"},"language":"en","primary_location":{"id":"doi:10.1137/s1064827595282350","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595282350","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5049797937","display_name":"Robert D. Skeel","orcid":"https://orcid.org/0000-0002-4807-8988"},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Robert D. Skeel","raw_affiliation_strings":["University of Illinois at Urbana Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Urbana Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101413810","display_name":"Guihua Zhang","orcid":"https://orcid.org/0000-0002-4599-418X"},"institutions":[{"id":"https://openalex.org/I57206974","display_name":"New York University","ror":"https://ror.org/0190ak572","country_code":"US","type":"education","lineage":["https://openalex.org/I57206974"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guihua Zhang","raw_affiliation_strings":["New York University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"New York University","institution_ids":["https://openalex.org/I57206974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5046513501","display_name":"Tamar Schlick","orcid":"https://orcid.org/0000-0002-2392-2062"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tamar Schlick","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.97,"has_fulltext":false,"cited_by_count":121,"citation_normalized_percentile":{"value":0.99163732,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":"18","issue":"1","first_page":"203","last_page":"222"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9613999724388123,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12277","display_name":"Frequency Control in Power Systems","score":0.9373999834060669,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/verlet-integration","display_name":"Verlet integration","score":0.9208492040634155},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8070751428604126},{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.7323542833328247},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.6587689518928528},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.5777862071990967},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5602773427963257},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5591565370559692},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.4659838080406189},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.4652911424636841},{"id":"https://openalex.org/keywords/variational-integrator","display_name":"Variational integrator","score":0.42712998390197754},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3471553325653076},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23786693811416626},{"id":"https://openalex.org/keywords/molecular-dynamics","display_name":"Molecular dynamics","score":0.1487463116645813},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.13792315125465393},{"id":"https://openalex.org/keywords/computational-chemistry","display_name":"Computational chemistry","score":0.09792166948318481},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.08350905776023865}],"concepts":[{"id":"https://openalex.org/C45600393","wikidata":"https://www.wikidata.org/wiki/Q2984997","display_name":"Verlet integration","level":3,"score":0.9208492040634155},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8070751428604126},{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.7323542833328247},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.6587689518928528},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.5777862071990967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5602773427963257},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5591565370559692},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.4659838080406189},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.4652911424636841},{"id":"https://openalex.org/C52154503","wikidata":"https://www.wikidata.org/wiki/Q7915797","display_name":"Variational integrator","level":4,"score":0.42712998390197754},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3471553325653076},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23786693811416626},{"id":"https://openalex.org/C59593255","wikidata":"https://www.wikidata.org/wiki/Q901663","display_name":"Molecular dynamics","level":2,"score":0.1487463116645813},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.13792315125465393},{"id":"https://openalex.org/C147597530","wikidata":"https://www.wikidata.org/wiki/Q369472","display_name":"Computational chemistry","level":1,"score":0.09792166948318481},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.08350905776023865},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s1064827595282350","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s1064827595282350","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.79.848","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.79.848","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://bionum.cs.uiuc.edu/SkZS97.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":29,"referenced_works":["https://openalex.org/W1528269930","https://openalex.org/W1655509865","https://openalex.org/W1975803620","https://openalex.org/W1983932107","https://openalex.org/W1989130537","https://openalex.org/W2003351322","https://openalex.org/W2005386550","https://openalex.org/W2017835622","https://openalex.org/W2024222447","https://openalex.org/W2025294553","https://openalex.org/W2030146934","https://openalex.org/W2031817405","https://openalex.org/W2034420901","https://openalex.org/W2041253741","https://openalex.org/W2041902442","https://openalex.org/W2046933294","https://openalex.org/W2052342858","https://openalex.org/W2062709451","https://openalex.org/W2067964076","https://openalex.org/W2073662751","https://openalex.org/W2082512436","https://openalex.org/W2082877496","https://openalex.org/W2084367325","https://openalex.org/W2107360721","https://openalex.org/W2126479355","https://openalex.org/W2142789340","https://openalex.org/W2323178299","https://openalex.org/W3022938717","https://openalex.org/W4255754126"],"related_works":["https://openalex.org/W2005694504","https://openalex.org/W2006096639","https://openalex.org/W3011672241","https://openalex.org/W2055660856","https://openalex.org/W1994054117","https://openalex.org/W2337185636","https://openalex.org/W2035154805","https://openalex.org/W2365493976","https://openalex.org/W4289288125","https://openalex.org/W2900876247"],"abstract_inverted_index":{"The":[0],"following":[1],"integration":[2],"methods":[3,36],"for":[4],"special":[5],"second-order":[6],"ordinary":[7],"differential":[8],"equations":[9],"are":[10,23,85],"studied:":[11],"leapfrog,":[12],"implicit":[13],"midpoint,":[14],"trapezoid,":[15],"St\u00f6rmer--Verlet,":[16],"and":[17,43,57,67,76,83,101],"Cowell--Numerov.":[18],"We":[19,52],"show":[20],"that":[21,74,108],"all":[22],"members,":[24,28],"or":[25],"equivalent":[26],"to":[27,98],"of":[29,33,49,64,70,90,112],"a":[30,46,55,68],"one-parameter":[31],"family":[32],"schemes.":[34],"Some":[35],"have":[37],"more":[38],"than":[39],"one":[40],"common":[41],"form,":[42],"we":[44,106],"discuss":[45],"systematic":[47],"enumeration":[48],"these":[50,95],"forms.":[51],"also":[53],"present":[54],"stability":[56],"accuracy":[58,100],"analysis":[59,111],"based":[60],"on":[61],"the":[62,91,109],"idea":[63],"\"modified":[65],"equations\"":[66],"proof":[69],"symplecticness.":[71],"It":[72],"follows":[73],"Cowell--Numerov":[75],"\"LIM2\"":[77],"(a":[78],"method":[79],"proposed":[80],"by":[81,94],"Zhang":[82],"Schlick)":[84],"symplectic.":[86],"A":[87],"different":[88],"interpretation":[89],"values":[92],"used":[93],"integrators":[96],"leads":[97],"higher":[99],"better":[102],"energy":[103,113],"conservation.":[104],"Hence,":[105],"suggest":[107],"straightforward":[110],"conservation":[114],"is":[115],"misleading.":[116]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":4},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
