{"id":"https://openalex.org/W4403786446","doi":"https://doi.org/10.1007/s10915-024-02702-2","title":"SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres","display_name":"SLERP-TVDRK (STVDRK) Methods for Ordinary Differential Equations on Spheres","publication_year":2024,"publication_date":"2024-10-26","ids":{"openalex":"https://openalex.org/W4403786446","doi":"https://doi.org/10.1007/s10915-024-02702-2"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-024-02702-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02702-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02702-2.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02702-2.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059208158","display_name":"Shingyu Leung","orcid":"https://orcid.org/0000-0002-4549-2761"},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Shingyu Leung","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China"],"raw_orcid":"https://orcid.org/0000-0002-4549-2761","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032129493","display_name":"Wai Ming Chau","orcid":null},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Wai Ming Chau","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5109503144","display_name":"Young Kyu Lee","orcid":null},"institutions":[{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Young Kyu Lee","raw_affiliation_strings":["Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5059208158"],"corresponding_institution_ids":["https://openalex.org/I200769079"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":2.0214,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.86712846,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":98},"biblio":{"volume":"101","issue":"3","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":0.9983999729156494,"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":0.9983999729156494,"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/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9980999827384949,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.996999979019165,"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/mathematics","display_name":"Mathematics","score":0.8844739198684692},{"id":"https://openalex.org/keywords/spheres","display_name":"SPHERES","score":0.7575960159301758},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.632331371307373},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4428616762161255},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41153091192245483},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.32320529222488403},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0597042441368103}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8844739198684692},{"id":"https://openalex.org/C72422203","wikidata":"https://www.wikidata.org/wiki/Q7392545","display_name":"SPHERES","level":2,"score":0.7575960159301758},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.632331371307373},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4428616762161255},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41153091192245483},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32320529222488403},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0597042441368103},{"id":"https://openalex.org/C1276947","wikidata":"https://www.wikidata.org/wiki/Q333","display_name":"Astronomy","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-024-02702-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02702-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02702-2.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-143839","is_oa":false,"landing_page_url":"http://repository.hkust.edu.hk/ir/Record/1783.1-143839","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"}],"best_oa_location":{"id":"doi:10.1007/s10915-024-02702-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-024-02702-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-024-02702-2.pdf","source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3042908541","display_name":null,"funder_award_id":"16302223","funder_id":"https://openalex.org/F4320329815","funder_display_name":"Hong Kong Government"},{"id":"https://openalex.org/G8768483371","display_name":null,"funder_award_id":"16300524","funder_id":"https://openalex.org/F4320329815","funder_display_name":"Hong Kong Government"}],"funders":[{"id":"https://openalex.org/F4320323537","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597"},{"id":"https://openalex.org/F4320329815","display_name":"Hong Kong Government","ror":"https://ror.org/034179816"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4403786446.pdf","grobid_xml":"https://content.openalex.org/works/W4403786446.grobid-xml"},"referenced_works_count":58,"referenced_works":["https://openalex.org/W28795493","https://openalex.org/W108778338","https://openalex.org/W166782598","https://openalex.org/W1480802543","https://openalex.org/W1509133757","https://openalex.org/W1553707579","https://openalex.org/W1723159182","https://openalex.org/W1901253971","https://openalex.org/W1969242270","https://openalex.org/W1969647398","https://openalex.org/W1987753869","https://openalex.org/W1995504856","https://openalex.org/W1997105074","https://openalex.org/W2001133651","https://openalex.org/W2009556859","https://openalex.org/W2010764244","https://openalex.org/W2011530793","https://openalex.org/W2015660465","https://openalex.org/W2019720983","https://openalex.org/W2019798593","https://openalex.org/W2022735385","https://openalex.org/W2029290244","https://openalex.org/W2039763880","https://openalex.org/W2041371172","https://openalex.org/W2042388195","https://openalex.org/W2047270043","https://openalex.org/W2049503034","https://openalex.org/W2049888254","https://openalex.org/W2055970595","https://openalex.org/W2059327423","https://openalex.org/W2062351484","https://openalex.org/W2067049166","https://openalex.org/W2075151302","https://openalex.org/W2078290517","https://openalex.org/W2089251565","https://openalex.org/W2093711514","https://openalex.org/W2099419572","https://openalex.org/W2099947152","https://openalex.org/W2116729868","https://openalex.org/W2128931829","https://openalex.org/W2129808720","https://openalex.org/W2132304268","https://openalex.org/W2137113506","https://openalex.org/W2144144709","https://openalex.org/W2151249889","https://openalex.org/W2155258047","https://openalex.org/W2156591439","https://openalex.org/W2165354764","https://openalex.org/W2168771200","https://openalex.org/W2581990426","https://openalex.org/W2787983785","https://openalex.org/W2936129870","https://openalex.org/W2962777248","https://openalex.org/W2964275135","https://openalex.org/W3010292040","https://openalex.org/W3046486801","https://openalex.org/W3193661195","https://openalex.org/W4213187341"],"related_works":["https://openalex.org/W3193357262","https://openalex.org/W2030434620","https://openalex.org/W2138488418","https://openalex.org/W2037987346","https://openalex.org/W2104617428","https://openalex.org/W2133684605","https://openalex.org/W1569572113","https://openalex.org/W3102283898","https://openalex.org/W1977478463","https://openalex.org/W2043671984"],"abstract_inverted_index":{"Abstract":[0],"We":[1],"mimic":[2],"the":[3,30,35,63,87,107,119,123],"conventional":[4],"explicit":[5],"Total":[6],"Variation":[7],"Diminishing":[8],"Runge\u2013Kutta":[9],"(TVDRK)":[10],"schemes":[11,79],"and":[12,37,68,126],"propose":[13],"a":[14,24,70],"class":[15],"of":[16,109],"numerical":[17],"integrators":[18],"to":[19,34,55,82],"solve":[20],"differential":[21],"equations":[22],"on":[23,122],"unit":[25,124],"sphere.":[26],"Our":[27],"approach":[28],"utilizes":[29],"exponential":[31],"map":[32],"inherent":[33],"sphere":[36,125],"employs":[38],"spherical":[39],"linear":[40],"interpolation":[41],"(SLERP).":[42],"These":[43],"modified":[44],"schemes,":[45],"named":[46],"SLERP-TVDRK":[47],"methods":[48],"or":[49],"STVDRK,":[50],"offer":[51],"improved":[52],"accuracy":[53],"compared":[54],"typical":[56],"projective":[57],"RK":[58],"methods.":[59],"Furthermore,":[60],"they":[61],"eliminate":[62],"need":[64],"for":[65,93],"any":[66],"projection":[67],"provide":[69],"straightforward":[71],"implementation.":[72],"While":[73],"we":[74,85,112],"have":[75],"successfully":[76],"constructed":[77],"STVDRK":[78],"only":[80],"up":[81],"third-order":[83],"accuracy,":[84],"explain":[86],"challenges":[88],"in":[89,117],"deriving":[90],"STVDRK-":[91],"r":[92],"$$r\\ge":[94],"4$$":[95],"<mml:math":[96],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\">":[97],"<mml:mrow>":[98],"<mml:mi>r</mml:mi>":[99],"<mml:mo>\u2265</mml:mo>":[100],"<mml:mn>4</mml:mn>":[101],"</mml:mrow>":[102],"</mml:math>":[103],".":[104],"To":[105],"showcase":[106],"effectiveness":[108],"our":[110,132],"approach,":[111],"will":[113],"demonstrate":[114],"its":[115],"application":[116],"solving":[118],"eikonal":[120],"equation":[121],"simulating":[127],"p":[128],"-harmonic":[129],"flows":[130],"using":[131],"proposed":[133],"method.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
