{"id":"https://openalex.org/W73701076","doi":"https://doi.org/10.1007/978-3-642-25255-6_25","title":"Parallel Fourth-Order Runge-Kutta Method to Solve Differential Equations","display_name":"Parallel Fourth-Order Runge-Kutta Method to Solve Differential Equations","publication_year":2011,"publication_date":"2011-01-01","ids":{"openalex":"https://openalex.org/W73701076","doi":"https://doi.org/10.1007/978-3-642-25255-6_25","mag":"73701076"},"language":"en","primary_location":{"id":"doi:10.1007/978-3-642-25255-6_25","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-25255-6_25","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"},"type":"book-chapter","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/A5100631260","display_name":"Chunfeng Liu","orcid":"https://orcid.org/0000-0001-8155-183X"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chunfeng Liu","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, Hebei, 063009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, Hebei, 063009, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028138545","display_name":"Haiming Wu","orcid":null},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Haiming Wu","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, Hebei, 063009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, Hebei, 063009, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5104095229","display_name":"Feng Li","orcid":"https://orcid.org/0009-0006-5091-6561"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li Feng","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, Hebei, 063009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, Hebei, 063009, China","institution_ids":["https://openalex.org/I137506752"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5048852821","display_name":"Aimin Yang","orcid":"https://orcid.org/0000-0003-0463-9023"},"institutions":[{"id":"https://openalex.org/I137506752","display_name":"North China University of Science and Technology","ror":"https://ror.org/04z4wmb81","country_code":"CN","type":"education","lineage":["https://openalex.org/I137506752"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Aimin Yang","raw_affiliation_strings":["College of Science, Hebei United University, Tangshan, Hebei, 063009, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"College of Science, Hebei United University, Tangshan, Hebei, 063009, China","institution_ids":["https://openalex.org/I137506752"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I137506752"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.05704698,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":null,"issue":null,"first_page":"192","last_page":"199"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9947999715805054,"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":0.9947999715805054,"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":0.9884999990463257,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9865999817848206,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.9037104845046997},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.6292332410812378},{"id":"https://openalex.org/keywords/dual","display_name":"Dual (grammatical number)","score":0.6106269359588623},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6024047136306763},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.48205313086509705},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.4599120020866394},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.442116379737854},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4376479387283325},{"id":"https://openalex.org/keywords/parallel-algorithm","display_name":"Parallel algorithm","score":0.4352206587791443},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.3867799639701843},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.34001463651657104},{"id":"https://openalex.org/keywords/computational-science","display_name":"Computational science","score":0.33088260889053345},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.2913869619369507},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1605617105960846},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.09877946972846985}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.9037104845046997},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.6292332410812378},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.6106269359588623},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6024047136306763},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.48205313086509705},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4599120020866394},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.442116379737854},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4376479387283325},{"id":"https://openalex.org/C120373497","wikidata":"https://www.wikidata.org/wiki/Q1087987","display_name":"Parallel algorithm","level":2,"score":0.4352206587791443},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.3867799639701843},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.34001463651657104},{"id":"https://openalex.org/C459310","wikidata":"https://www.wikidata.org/wiki/Q117801","display_name":"Computational science","level":1,"score":0.33088260889053345},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2913869619369507},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1605617105960846},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.09877946972846985},{"id":"https://openalex.org/C142362112","wikidata":"https://www.wikidata.org/wiki/Q735","display_name":"Art","level":0,"score":0.0},{"id":"https://openalex.org/C124952713","wikidata":"https://www.wikidata.org/wiki/Q8242","display_name":"Literature","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-3-642-25255-6_25","is_oa":false,"landing_page_url":"https://doi.org/10.1007/978-3-642-25255-6_25","pdf_url":null,"source":{"id":"https://openalex.org/S106296714","display_name":"Lecture notes in computer science","issn_l":"0302-9743","issn":["0302-9743","1611-3349"],"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":"book series"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Lecture Notes in Computer Science","raw_type":"book-chapter"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":7,"referenced_works":["https://openalex.org/W2021667116","https://openalex.org/W2070366559","https://openalex.org/W2095198524","https://openalex.org/W2188107347","https://openalex.org/W2366431484","https://openalex.org/W2393313905","https://openalex.org/W2540601962"],"related_works":["https://openalex.org/W4211042180","https://openalex.org/W832825236","https://openalex.org/W2378531610","https://openalex.org/W2295655673","https://openalex.org/W181143595","https://openalex.org/W2956395387","https://openalex.org/W3017026185","https://openalex.org/W2052381424","https://openalex.org/W2136451125","https://openalex.org/W1994850555"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2015,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}
