{"id":"https://openalex.org/W4213025979","doi":"https://doi.org/10.3390/sym14020365","title":"MGPS: Midpoint-Series Group Preserving Scheme for Discretizing Nonlinear Dynamics","display_name":"MGPS: Midpoint-Series Group Preserving Scheme for Discretizing Nonlinear Dynamics","publication_year":2022,"publication_date":"2022-02-12","ids":{"openalex":"https://openalex.org/W4213025979","doi":"https://doi.org/10.3390/sym14020365"},"language":"en","primary_location":{"id":"doi:10.3390/sym14020365","doi":"https://doi.org/10.3390/sym14020365","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020365","pdf_url":"https://www.mdpi.com/2073-8994/14/2/365/pdf?version=1645422875","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/14/2/365/pdf?version=1645422875","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5025615478","display_name":"Zhenxing Xu","orcid":"https://orcid.org/0000-0002-8473-1753","observed_orcids":["https://orcid.org/0000-0002-8473-1753"]},"institutions":[{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhenxing Xu","raw_affiliation_strings":["Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China","School of Computing Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0002-8473-1753","affiliations":[{"raw_affiliation_string":"Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"School of Computing Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101603157","display_name":"Jinzhao Wu","orcid":"https://orcid.org/0000-0002-5654-4870","observed_orcids":["https://orcid.org/0000-0002-5654-4870"]},"institutions":[{"id":"https://openalex.org/I167274908","display_name":"Guangxi Minzu University","ror":"https://ror.org/0495efn48","country_code":"CN","type":"education","lineage":["https://openalex.org/I167274908"]},{"id":"https://openalex.org/I19820366","display_name":"Chinese Academy of Sciences","ror":"https://ror.org/034t30j35","country_code":"CN","type":"government","lineage":["https://openalex.org/I19820366"]},{"id":"https://openalex.org/I4210165038","display_name":"University of Chinese Academy of Sciences","ror":"https://ror.org/05qbk4x57","country_code":"CN","type":"education","lineage":["https://openalex.org/I19820366","https://openalex.org/I4210165038"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Jinzhao Wu","raw_affiliation_strings":["Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China","Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China","School of Computing Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China"],"raw_orcid":"https://orcid.org/0000-0002-5654-4870","affiliations":[{"raw_affiliation_string":"Chengdu Institute of Computer Application, Chinese Academy of Sciences, Chengdu 610041, China","institution_ids":["https://openalex.org/I19820366"]},{"raw_affiliation_string":"Guangxi Key Laboratory of Hybrid Computation and IC Design Analysis, Guangxi University for Nationalities, Nanning 530006, China","institution_ids":["https://openalex.org/I167274908"]},{"raw_affiliation_string":"School of Computing Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China","institution_ids":["https://openalex.org/I4210165038"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5101603157"],"corresponding_institution_ids":["https://openalex.org/I167274908","https://openalex.org/I19820366","https://openalex.org/I4210165038"],"apc_list":{"value":1800,"currency":"CHF","value_usd":1885},"apc_paid":{"value":1800,"currency":"CHF","value_usd":1885},"fwci":0.3863,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.41986795,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":88,"max":93},"biblio":{"volume":"14","issue":"2","first_page":"365","last_page":"365"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary 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 Solvers for Ordinary 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/T12727","display_name":"Singular Perturbation, Asymptotics and Difference Schemes","score":0.0,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.0,"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/ordinary-differential-equations","display_name":"ordinary differential equations","score":0.800000011920929},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"initial value problems","score":0.9589999914169312},{"id":"https://openalex.org/keywords/nonlinear-dynamical-systems","display_name":"nonlinear dynamical systems","score":0.7879999876022339},{"id":"https://openalex.org/keywords/midpoint-rule","display_name":"midpoint rule","score":0.7570000290870667},{"id":"https://openalex.org/keywords/symmetry-groups","display_name":"symmetry groups","score":0.46700000762939453},{"id":"https://openalex.org/keywords/spurious-solutions","display_name":"spurious solutions","score":0.6169999837875366},{"id":"https://openalex.org/keywords/error-analysis","display_name":"error analysis","score":0.7149999737739563},{"id":"https://openalex.org/keywords/stability-analysis","display_name":"stability analysis","score":0.9559999704360962},{"id":"https://openalex.org/keywords/convergence","display_name":"convergence","score":0.7160000205039978},{"id":"https://openalex.org/keywords/periodic-hamiltonian-systems","display_name":"periodic Hamiltonian systems","score":0.972000002861023}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.74078369140625},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6642985343933105},{"id":"https://openalex.org/C34130140","wikidata":"https://www.wikidata.org/wiki/Q1645406","display_name":"Midpoint","level":2,"score":0.647903323173523},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5715311765670776},{"id":"https://openalex.org/C85807060","wikidata":"https://www.wikidata.org/wiki/Q17103851","display_name":"Midpoint method","level":2,"score":0.5080866813659668},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5043712854385376},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4948806166648865},{"id":"https://openalex.org/C2781311116","wikidata":"https://www.wikidata.org/wiki/Q83306","display_name":"Group (periodic table)","level":2,"score":0.4860866367816925},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.47800055146217346},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.43867695331573486},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.42427384853363037},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.36153116822242737},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3505255877971649},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3191377520561218},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.28762614727020264},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14725133776664734},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07626986503601074},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym14020365","doi":"https://doi.org/10.3390/sym14020365","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020365","pdf_url":"https://www.mdpi.com/2073-8994/14/2/365/pdf?version=1645422875","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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:45ff7f070ba747158c60c85d7dc803b2","doi":null,"is_oa":true,"landing_page_url":"https://doaj.org/article/45ff7f070ba747158c60c85d7dc803b2","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"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 14, Iss 2, p 365 (2022)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym14020365","doi":"https://doi.org/10.3390/sym14020365","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym14020365","pdf_url":"https://www.mdpi.com/2073-8994/14/2/365/pdf?version=1645422875","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,"listed_in":["anvur-scientific","cwts-core","norway-1","poland-70","russia-white-list-1","vabb-shw"],"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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3580067134","display_name":null,"funder_award_id":"AA17204096","funder_id":"https://openalex.org/F4320335965","funder_display_name":"Science and Technology Major Project of Guangxi"},{"id":"https://openalex.org/G8034016658","display_name":null,"funder_award_id":"61772006","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"},{"id":"https://openalex.org/F4320335965","display_name":"Science and Technology Major Project of Guangxi","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4213025979.pdf","grobid_xml":"https://content.openalex.org/works/W4213025979.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W1489199834","https://openalex.org/W1499853177","https://openalex.org/W1534714322","https://openalex.org/W1569692898","https://openalex.org/W1604596197","https://openalex.org/W1772466691","https://openalex.org/W1905380539","https://openalex.org/W1965357780","https://openalex.org/W1972404575","https://openalex.org/W1975630497","https://openalex.org/W2021627653","https://openalex.org/W2028547335","https://openalex.org/W2032405498","https://openalex.org/W2049664307","https://openalex.org/W2075752478","https://openalex.org/W2129965357","https://openalex.org/W2152533774","https://openalex.org/W2176215692","https://openalex.org/W2441183164","https://openalex.org/W2522902416","https://openalex.org/W2945156329","https://openalex.org/W4236306094"],"related_works":["https://openalex.org/W3002073230","https://openalex.org/W2013202784","https://openalex.org/W2300987354","https://openalex.org/W2004118536","https://openalex.org/W4306850863","https://openalex.org/W1989130537","https://openalex.org/W2257540973","https://openalex.org/W2008860580","https://openalex.org/W2094325540","https://openalex.org/W2581452175"],"abstract_inverted_index":{"In":[0],"this":[1],"article,":[2],"we":[3,76],"propose":[4],"a":[5],"new":[6],"computational":[7],"method":[8],"for":[9],"initial":[10],"value":[11],"problems":[12],"in":[13],"ordinary":[14],"differential":[15],"equations.":[16],"The":[17,55],"algorithm":[18,79],"combines":[19],"the":[20,23,30,38,42,46,51,64,68,72,78,98],"merits":[21],"of":[22,32,45,67],"group":[24],"preserving":[25],"scheme":[26],"(GPS),":[27],"which":[28],"has":[29],"ability":[31,91],"avoiding":[33],"possible":[34],"spurious":[35],"solutions":[36],"utilizing":[37],"inherent":[39],"symmetry":[40],"group,":[41],"cone":[43],"structure":[44],"nonlinear":[47],"dynamical":[48],"system,":[49],"and":[50,57,87],"classic":[52],"midpoint":[53],"rule.":[54],"error":[56],"stability":[58],"analysis":[59],"are":[60],"included":[61],"to":[62,83],"demonstrate":[63],"convergence":[65],"properties":[66],"presented":[69],"method.":[70],"From":[71],"numerical":[73],"experimental":[74],"results":[75],"obtained,":[77],"can":[80],"be":[81,84],"said":[82],"computationally":[85],"effective":[86],"possesses":[88],"better":[89],"simulation":[90],"generally.":[92],"Meanwhile,":[93],"it":[94],"works":[95],"well":[96],"with":[97],"periodic":[99],"Hamiltonian":[100],"system.":[101]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-02-24T00:00:00"}