{"id":"https://openalex.org/W2912385764","doi":"https://doi.org/10.3390/sym11020142","title":"Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems","display_name":"Symplectic Effective Order Numerical Methods for Separable Hamiltonian Systems","publication_year":2019,"publication_date":"2019-01-28","ids":{"openalex":"https://openalex.org/W2912385764","doi":"https://doi.org/10.3390/sym11020142","mag":"2912385764"},"language":"en","primary_location":{"id":"doi:10.3390/sym11020142","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020142","pdf_url":"https://www.mdpi.com/2073-8994/11/2/142/pdf?version=1548670181","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/11/2/142/pdf?version=1548670181","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100741107","display_name":"Junaid Ahmad","orcid":"https://orcid.org/0000-0003-4916-5829"},"institutions":[{"id":"https://openalex.org/I142732210","display_name":"University of Engineering and Technology Lahore","ror":"https://ror.org/0051w2v06","country_code":"PK","type":"education","lineage":["https://openalex.org/I142732210"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Junaid Ahmad","raw_affiliation_strings":["Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan","institution_ids":["https://openalex.org/I142732210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060002626","display_name":"Yousaf Habib","orcid":"https://orcid.org/0000-0003-1709-1159"},"institutions":[{"id":"https://openalex.org/I16076960","display_name":"COMSATS University Islamabad","ror":"https://ror.org/00nqqvk19","country_code":"PK","type":"education","lineage":["https://openalex.org/I16076960"]},{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":true,"raw_author_name":"Yousaf Habib","raw_affiliation_strings":["Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 45550, Pakistan","School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore 45550, Pakistan","institution_ids":["https://openalex.org/I16076960"]},{"raw_affiliation_string":"School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101888922","display_name":"Shafiq Ur Rehman","orcid":"https://orcid.org/0000-0002-7656-0456"},"institutions":[{"id":"https://openalex.org/I142732210","display_name":"University of Engineering and Technology Lahore","ror":"https://ror.org/0051w2v06","country_code":"PK","type":"education","lineage":["https://openalex.org/I142732210"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Shafiq ur Rehman","raw_affiliation_strings":["Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Engineering and Technology, Lahore 54890, Pakistan","institution_ids":["https://openalex.org/I142732210"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083900670","display_name":"Azqa Arif","orcid":null},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Azqa Arif","raw_affiliation_strings":["School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan"],"affiliations":[{"raw_affiliation_string":"School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085354508","display_name":"Saba Shafiq","orcid":null},"institutions":[{"id":"https://openalex.org/I929597975","display_name":"National University of Sciences and Technology","ror":"https://ror.org/03w2j5y17","country_code":"PK","type":"education","lineage":["https://openalex.org/I929597975"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Saba Shafiq","raw_affiliation_strings":["School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan"],"affiliations":[{"raw_affiliation_string":"School of Natural Sciences, Department of Mathematics, National University of Sciences and Technology, Islamabad 44000, Pakistan","institution_ids":["https://openalex.org/I929597975"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025702714","display_name":"Muhammad Younas","orcid":null},"institutions":[{"id":"https://openalex.org/I79571142","display_name":"Virtual University of Pakistan","ror":"https://ror.org/00ya1zd25","country_code":"PK","type":"education","lineage":["https://openalex.org/I79571142"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Muhammad Younas","raw_affiliation_strings":["Business Administration Programme, Virtual University of Pakistan, Lahore 54000, Pakistan"],"affiliations":[{"raw_affiliation_string":"Business Administration Programme, Virtual University of Pakistan, Lahore 54000, Pakistan","institution_ids":["https://openalex.org/I79571142"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":["https://openalex.org/A5060002626"],"corresponding_institution_ids":["https://openalex.org/I16076960","https://openalex.org/I929597975"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.3246,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.49757225,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"2","first_page":"142","last_page":"142"},"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9972000122070312,"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"}},{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9943000078201294,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/symplectic-geometry","display_name":"Symplectic geometry","score":0.8975057601928711},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.7889295816421509},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.7510327100753784},{"id":"https://openalex.org/keywords/hamiltonian-system","display_name":"Hamiltonian system","score":0.7369773983955383},{"id":"https://openalex.org/keywords/symplectic-integrator","display_name":"Symplectic integrator","score":0.7045241594314575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5773540735244751},{"id":"https://openalex.org/keywords/hamiltonian","display_name":"Hamiltonian (control theory)","score":0.5593603253364563},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.55221027135849},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.4155062437057495},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.40933701395988464},{"id":"https://openalex.org/keywords/symplectic-manifold","display_name":"Symplectic manifold","score":0.34692537784576416},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.299793004989624},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2657470107078552}],"concepts":[{"id":"https://openalex.org/C168619227","wikidata":"https://www.wikidata.org/wiki/Q2190991","display_name":"Symplectic geometry","level":2,"score":0.8975057601928711},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.7889295816421509},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.7510327100753784},{"id":"https://openalex.org/C121770821","wikidata":"https://www.wikidata.org/wiki/Q2072471","display_name":"Hamiltonian system","level":2,"score":0.7369773983955383},{"id":"https://openalex.org/C207646825","wikidata":"https://www.wikidata.org/wiki/Q7661847","display_name":"Symplectic integrator","level":4,"score":0.7045241594314575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5773540735244751},{"id":"https://openalex.org/C130787639","wikidata":"https://www.wikidata.org/wiki/Q5645293","display_name":"Hamiltonian (control theory)","level":2,"score":0.5593603253364563},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.55221027135849},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4155062437057495},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.40933701395988464},{"id":"https://openalex.org/C130190758","wikidata":"https://www.wikidata.org/wiki/Q1064500","display_name":"Symplectic manifold","level":3,"score":0.34692537784576416},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.299793004989624},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2657470107078552}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym11020142","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020142","pdf_url":"https://www.mdpi.com/2073-8994/11/2/142/pdf?version=1548670181","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:ac0cfbc6f77b4746af671ac5a03ef8a2","is_oa":true,"landing_page_url":"https://doaj.org/article/ac0cfbc6f77b4746af671ac5a03ef8a2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 11, Iss 2, p 142 (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym11020142","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym11020142","pdf_url":"https://www.mdpi.com/2073-8994/11/2/142/pdf?version=1548670181","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.550000011920929,"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2912385764.pdf","grobid_xml":"https://content.openalex.org/works/W2912385764.grobid-xml"},"referenced_works_count":15,"referenced_works":["https://openalex.org/W100188788","https://openalex.org/W130410985","https://openalex.org/W1987155717","https://openalex.org/W1994923027","https://openalex.org/W2039780643","https://openalex.org/W2047267990","https://openalex.org/W2084367325","https://openalex.org/W2107360721","https://openalex.org/W2148437017","https://openalex.org/W2155579513","https://openalex.org/W2586710356","https://openalex.org/W3209416867","https://openalex.org/W4300831640","https://openalex.org/W6628152718","https://openalex.org/W6986175198"],"related_works":["https://openalex.org/W1994184409","https://openalex.org/W2005670812","https://openalex.org/W3011215806","https://openalex.org/W2071757030","https://openalex.org/W1982322958","https://openalex.org/W2297672260","https://openalex.org/W2054703718","https://openalex.org/W1968584667","https://openalex.org/W54222547","https://openalex.org/W2147685202"],"abstract_inverted_index":{"A":[0,35],"family":[1],"of":[2,18,37,47],"explicit":[3,24],"symplectic":[4,31],"partitioned":[5],"Runge-Kutta":[6,33],"methods":[7,25],"are":[8,26],"derived":[9],"with":[10,53],"effective":[11],"order":[12],"3":[13],"for":[14],"the":[15,45,48],"numerical":[16,38],"integration":[17],"separable":[19,41],"Hamiltonian":[20,42],"systems.":[21],"The":[22],"proposed":[23],"more":[27],"efficient":[28],"than":[29],"existing":[30],"implicit":[32],"methods.":[34],"selection":[36],"experiments":[39],"on":[40],"system":[43],"confirming":[44],"efficiency":[46],"approach":[49],"is":[50],"also":[51],"provided":[52],"good":[54],"energy":[55],"conservation.":[56]},"counts_by_year":[{"year":2019,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}