{"id":"https://openalex.org/W2141124203","doi":"https://doi.org/10.1007/s00211-008-0170-x","title":"Generating functions of multi-symplectic RK methods via DW Hamilton\u2013Jacobi equations","display_name":"Generating functions of multi-symplectic RK methods via DW Hamilton\u2013Jacobi equations","publication_year":2008,"publication_date":"2008-08-12","ids":{"openalex":"https://openalex.org/W2141124203","doi":"https://doi.org/10.1007/s00211-008-0170-x","mag":"2141124203"},"language":"en","primary_location":{"id":"doi:10.1007/s00211-008-0170-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-008-0170-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","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/A5018970203","display_name":"Jialin Hong","orcid":"https://orcid.org/0000-0002-9664-6361"},"institutions":[{"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":true,"raw_author_name":"Jialin Hong","raw_affiliation_strings":["LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, 100190, Beijing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, 100190, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111558080","display_name":"Yajuan Sun","orcid":"https://orcid.org/0000-0003-1599-600X"},"institutions":[{"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":"Yajuan Sun","raw_affiliation_strings":["LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China","Academy of Mathematics and Systems Science, Chinese Academy of Sciences, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, 100190, Beijing, China#TAB#"],"affiliations":[{"raw_affiliation_string":"LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, 100190, Beijing, China","institution_ids":["https://openalex.org/I4210120485","https://openalex.org/I19820366"]},{"raw_affiliation_string":"Academy of Mathematics and Systems Science, Chinese Academy of Sciences, LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, 100190, Beijing, China#TAB#","institution_ids":["https://openalex.org/I19820366"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5018970203"],"corresponding_institution_ids":["https://openalex.org/I19820366","https://openalex.org/I4210120485"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.5149,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.7080209,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"110","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":1.0,"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":1.0,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9986000061035156,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.8606893420219421},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.837120771408081},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.756196141242981},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5987645387649536},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.5137010812759399},{"id":"https://openalex.org/keywords/jacobi-method","display_name":"Jacobi method","score":0.5035173296928406},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.49696043133735657},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.488429456949234},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.42367714643478394},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4057195782661438},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.36348867416381836},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3573644757270813},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.31720542907714844},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.10208383202552795},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.08828204870223999}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8606893420219421},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.837120771408081},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.756196141242981},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5987645387649536},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.5137010812759399},{"id":"https://openalex.org/C67923128","wikidata":"https://www.wikidata.org/wiki/Q1481893","display_name":"Jacobi method","level":2,"score":0.5035173296928406},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.49696043133735657},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.488429456949234},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42367714643478394},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4057195782661438},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.36348867416381836},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3573644757270813},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.31720542907714844},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.10208383202552795},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.08828204870223999}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s00211-008-0170-x","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s00211-008-0170-x","pdf_url":null,"source":{"id":"https://openalex.org/S4210205683","display_name":"Numerische Mathematik","issn_l":"0029-599X","issn":["0029-599X","0945-3245"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerische Mathematik","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W75417299","https://openalex.org/W750652296","https://openalex.org/W1524565983","https://openalex.org/W1530404001","https://openalex.org/W1539055555","https://openalex.org/W1544770838","https://openalex.org/W1559545894","https://openalex.org/W1559840026","https://openalex.org/W1573927207","https://openalex.org/W1968640936","https://openalex.org/W1969568683","https://openalex.org/W2031055124","https://openalex.org/W2031836732","https://openalex.org/W2039078443","https://openalex.org/W2046608570","https://openalex.org/W2068002984","https://openalex.org/W2075892504","https://openalex.org/W2080091608","https://openalex.org/W2084367325","https://openalex.org/W2112405917","https://openalex.org/W2126136838","https://openalex.org/W2140801273","https://openalex.org/W2151063181","https://openalex.org/W2156910197","https://openalex.org/W2170039048","https://openalex.org/W2291400263","https://openalex.org/W2313810294","https://openalex.org/W2341885715","https://openalex.org/W2374612378","https://openalex.org/W2489032104","https://openalex.org/W2588671166","https://openalex.org/W2766780695","https://openalex.org/W3092549130","https://openalex.org/W3099153488","https://openalex.org/W3123419175","https://openalex.org/W4229672964","https://openalex.org/W4230093189"],"related_works":["https://openalex.org/W1989001262","https://openalex.org/W3203832079","https://openalex.org/W2083752714","https://openalex.org/W1580949276","https://openalex.org/W2952936160","https://openalex.org/W781098179","https://openalex.org/W1479893480","https://openalex.org/W4300176601","https://openalex.org/W2958114100","https://openalex.org/W2140857796"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":2},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}