{"id":"https://openalex.org/W1481268870","doi":"https://doi.org/10.1007/bfb0057930","title":"Waveform relaxation for second order differential equation y\u2032\u2019=f(x,y)","display_name":"Waveform relaxation for second order differential equation y\u2032\u2019=f(x,y)","publication_year":1998,"publication_date":"1998-01-01","ids":{"openalex":"https://openalex.org/W1481268870","doi":"https://doi.org/10.1007/bfb0057930","mag":"1481268870"},"language":"en","primary_location":{"id":"doi:10.1007/bfb0057930","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bfb0057930","pdf_url":"https://link.springer.com/content/pdf/10.1007/BFb0057930.pdf","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":true,"oa_status":"bronze","oa_url":"https://link.springer.com/content/pdf/10.1007/BFb0057930.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078115366","display_name":"Kazufumi Ozawa","orcid":null},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":true,"raw_author_name":"Kazufumi Ozawa","raw_affiliation_strings":["Graduate School of Information Science, Tohoku University, Kawauchi, 980-8576, Sendai, Japan","Graduate School of Information Science, TOHOKU University, Sendai, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science, Tohoku University, Kawauchi, 980-8576, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Graduate School of Information Science, TOHOKU University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101647651","display_name":"Susumu Yamada","orcid":"https://orcid.org/0000-0002-3551-9422"},"institutions":[{"id":"https://openalex.org/I201537933","display_name":"Tohoku University","ror":"https://ror.org/01dq60k83","country_code":"JP","type":"education","lineage":["https://openalex.org/I201537933"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Susumu Yamada","raw_affiliation_strings":["Graduate School of Information Science, Tohoku University, Kawauchi, 980-8576, Sendai, Japan","Graduate School of Information Science, TOHOKU University, Sendai, Japan"],"affiliations":[{"raw_affiliation_string":"Graduate School of Information Science, Tohoku University, Kawauchi, 980-8576, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]},{"raw_affiliation_string":"Graduate School of Information Science, TOHOKU University, Sendai, Japan","institution_ids":["https://openalex.org/I201537933"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078115366"],"corresponding_institution_ids":["https://openalex.org/I201537933"],"apc_list":{"value":5000,"currency":"EUR","value_usd":5392},"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":1,"citation_normalized_percentile":{"value":0.16216216,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"780","last_page":"787"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9983999729156494,"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":0.9977999925613403,"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/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.8356063365936279},{"id":"https://openalex.org/keywords/waveform","display_name":"Waveform","score":0.7712901830673218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6556078195571899},{"id":"https://openalex.org/keywords/relaxation","display_name":"Relaxation (psychology)","score":0.6278408765792847},{"id":"https://openalex.org/keywords/quadratic-growth","display_name":"Quadratic growth","score":0.5505306720733643},{"id":"https://openalex.org/keywords/speedup","display_name":"Speedup","score":0.5339969396591187},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5003910064697266},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.495022714138031},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.45030155777931213},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35063764452934265},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.24300402402877808},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10888174176216125}],"concepts":[{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.8356063365936279},{"id":"https://openalex.org/C197424946","wikidata":"https://www.wikidata.org/wiki/Q1165717","display_name":"Waveform","level":3,"score":0.7712901830673218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6556078195571899},{"id":"https://openalex.org/C2776029896","wikidata":"https://www.wikidata.org/wiki/Q3935810","display_name":"Relaxation (psychology)","level":2,"score":0.6278408765792847},{"id":"https://openalex.org/C195956108","wikidata":"https://www.wikidata.org/wiki/Q7268362","display_name":"Quadratic growth","level":2,"score":0.5505306720733643},{"id":"https://openalex.org/C68339613","wikidata":"https://www.wikidata.org/wiki/Q1549489","display_name":"Speedup","level":2,"score":0.5339969396591187},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5003910064697266},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.495022714138031},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.45030155777931213},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35063764452934265},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.24300402402877808},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10888174176216125},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C165801399","wikidata":"https://www.wikidata.org/wiki/Q25428","display_name":"Voltage","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/bfb0057930","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bfb0057930","pdf_url":"https://link.springer.com/content/pdf/10.1007/BFb0057930.pdf","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":{"id":"doi:10.1007/bfb0057930","is_oa":true,"landing_page_url":"https://doi.org/10.1007/bfb0057930","pdf_url":"https://link.springer.com/content/pdf/10.1007/BFb0057930.pdf","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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1481268870.pdf","grobid_xml":"https://content.openalex.org/works/W1481268870.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W9124626","https://openalex.org/W1509997287","https://openalex.org/W2023344463","https://openalex.org/W2042388195","https://openalex.org/W2071225300","https://openalex.org/W2140779530","https://openalex.org/W3209416867","https://openalex.org/W4213104200"],"related_works":["https://openalex.org/W2058965144","https://openalex.org/W2164382479","https://openalex.org/W98480971","https://openalex.org/W2150291671","https://openalex.org/W2027972911","https://openalex.org/W2146343568","https://openalex.org/W2013643406","https://openalex.org/W2157978810","https://openalex.org/W2597809628","https://openalex.org/W3046370962"],"abstract_inverted_index":null,"counts_by_year":[{"year":2018,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}