{"id":"https://openalex.org/W1969568683","doi":"https://doi.org/10.1090/s0025-5718-05-01793-x","title":"The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs","display_name":"The multi-symplecticity of partitioned Runge-Kutta methods for Hamiltonian PDEs","publication_year":2005,"publication_date":"2005-09-29","ids":{"openalex":"https://openalex.org/W1969568683","doi":"https://doi.org/10.1090/s0025-5718-05-01793-x","mag":"1969568683"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-05-01793-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01793-x","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01793-X/S0025-5718-05-01793-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01793-X/S0025-5718-05-01793-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018970203","display_name":"Jialin Hong","orcid":"https://orcid.org/0000-0002-9664-6361"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jialin Hong","raw_affiliation_strings":["State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","Chinese Academy of Sciences, Beijing, China"],"affiliations":[{"raw_affiliation_string":"State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, P.O.Box 2719, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Chinese Academy of Sciences, Beijing, China","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025082141","display_name":"Hongyu Liu","orcid":"https://orcid.org/0000-0002-2930-3510"},"institutions":[{"id":"https://openalex.org/I177725633","display_name":"Chinese University of Hong Kong","ror":"https://ror.org/00t33hh48","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyu Liu","raw_affiliation_strings":["Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u00e2\u0080\u0099s Republic of China","Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u2019s Republic of China","Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I177725633"]},{"raw_affiliation_string":"Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Department of Mathematics, The Chinese University of Hong Kong, Hong Kong, People\u2019s Republic of China","institution_ids":["https://openalex.org/I177725633"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023167307","display_name":"Geng Sun","orcid":"https://orcid.org/0000-0001-6713-5151"},"institutions":[{"id":"https://openalex.org/I4210120485","display_name":"Academy of Mathematics and Systems Science","ror":"https://ror.org/02jkmyk67","country_code":"CN","type":"facility","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210120485"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"funder","lineage":["https://openalex.org/I19820366"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Geng Sun","raw_affiliation_strings":["Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u2019s Republic of China"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u00e2\u0080\u0099s Republic of China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Institute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, People\u2019s Republic of China","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5018970203"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":null,"apc_paid":null,"fwci":4.7428,"has_fulltext":true,"cited_by_count":50,"citation_normalized_percentile":{"value":0.95382944,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"75","issue":"253","first_page":"167","last_page":"181"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9979000091552734,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9914000034332275,"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/mathematics","display_name":"Mathematics","score":0.7981248497962952},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7697471976280212},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.683936357498169},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.6145399212837219},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.6087460517883301},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4652617275714874},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3494557738304138},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.29000476002693176},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.13720065355300903}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7981248497962952},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7697471976280212},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.683936357498169},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.6145399212837219},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.6087460517883301},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4652617275714874},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3494557738304138},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.29000476002693176},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.13720065355300903}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1090/s0025-5718-05-01793-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01793-x","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01793-X/S0025-5718-05-01793-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.153.68","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.153.68","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.ams.org/mcom/2006-75-253/S0025-5718-05-01793-X/S0025-5718-05-01793-X.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-05-01793-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-05-01793-x","pdf_url":"https://www.ams.org/mcom/2006-75-253/S0025-5718-05-01793-X/S0025-5718-05-01793-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G20074338","display_name":null,"funder_award_id":"10371128","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6058138561","display_name":null,"funder_award_id":", No.","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8504493569","display_name":null,"funder_award_id":"19971089","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1969568683.pdf","grobid_xml":"https://content.openalex.org/works/W1969568683.grobid-xml"},"referenced_works_count":19,"referenced_works":["https://openalex.org/W1544770838","https://openalex.org/W1575549230","https://openalex.org/W1974134022","https://openalex.org/W1975034694","https://openalex.org/W1981247295","https://openalex.org/W1986367849","https://openalex.org/W1999698136","https://openalex.org/W2006042718","https://openalex.org/W2008007187","https://openalex.org/W2028693999","https://openalex.org/W2037864736","https://openalex.org/W2048129990","https://openalex.org/W2080091608","https://openalex.org/W2081702207","https://openalex.org/W2084367325","https://openalex.org/W2170039048","https://openalex.org/W2515471313","https://openalex.org/W2981569720","https://openalex.org/W3092437347"],"related_works":["https://openalex.org/W4206768127","https://openalex.org/W4213270568","https://openalex.org/W4244999877","https://openalex.org/W4301315183","https://openalex.org/W2083551655","https://openalex.org/W2157764110","https://openalex.org/W2121498459","https://openalex.org/W2811272663","https://openalex.org/W1989572481","https://openalex.org/W2071286043"],"abstract_inverted_index":{"In":[0],"this":[1],"article":[2],"we":[3],"consider":[4],"partitioned":[5],"Runge-Kutta":[6],"(PRK)":[7],"methods":[8,24],"for":[9,20],"Hamiltonian":[10,26],"partial":[11],"differential":[12],"equations":[13],"(PDEs)":[14],"and":[15],"present":[16],"some":[17],"sufficient":[18],"conditions":[19],"multi-symplecticity":[21],"of":[22,25],"PRK":[23],"PDEs.":[27]},"counts_by_year":[{"year":2025,"cited_by_count":3},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}