{"id":"https://openalex.org/W2039558415","doi":"https://doi.org/10.1137/s106482759833601x","title":"Runge--Kutta Solutions of a Hyperbolic Conservation Law with Source Term","display_name":"Runge--Kutta Solutions of a Hyperbolic Conservation Law with Source Term","publication_year":2000,"publication_date":"2000-01-01","ids":{"openalex":"https://openalex.org/W2039558415","doi":"https://doi.org/10.1137/s106482759833601x","mag":"2039558415"},"language":"en","primary_location":{"id":"doi:10.1137/s106482759833601x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759833601x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://discovery.dundee.ac.uk/ws/files/89178/NA180_MAA_DFG_DJH.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048581232","display_name":"Mark A. Aves","orcid":null},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Mark A. Aves","raw_affiliation_strings":["University of Dundee"],"affiliations":[{"raw_affiliation_string":"University of Dundee","institution_ids":["https://openalex.org/I177639307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103592010","display_name":"David F. Griffiths","orcid":null},"institutions":[{"id":"https://openalex.org/I177639307","display_name":"University of Dundee","ror":"https://ror.org/03h2bxq36","country_code":"GB","type":"education","lineage":["https://openalex.org/I177639307"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"David F. Griffiths","raw_affiliation_strings":["University of Dundee"],"affiliations":[{"raw_affiliation_string":"University of Dundee","institution_ids":["https://openalex.org/I177639307"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5058486589","display_name":"Desmond J. Higham","orcid":"https://orcid.org/0000-0002-6635-3461"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Desmond J. Higham","raw_affiliation_strings":["Mathematics And Statistics"],"affiliations":[{"raw_affiliation_string":"Mathematics And Statistics","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5048581232"],"corresponding_institution_ids":["https://openalex.org/I177639307"],"apc_list":null,"apc_paid":null,"fwci":1.1055,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.76945971,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"22","issue":"1","first_page":"20","last_page":"38"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9980000257492065,"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"}},"topics":[{"id":"https://openalex.org/T10173","display_name":"Computational Fluid Dynamics and Aerodynamics","score":0.9980000257492065,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.9973000288009644,"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/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.994700014591217,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.8820323944091797},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.820318341255188},{"id":"https://openalex.org/keywords/conservation-law","display_name":"Conservation law","score":0.7871387600898743},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.7416922450065613},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.704026997089386},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6389322876930237},{"id":"https://openalex.org/keywords/jump","display_name":"Jump","score":0.5968598127365112},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5766567587852478},{"id":"https://openalex.org/keywords/hyperbolic-partial-differential-equation","display_name":"Hyperbolic partial differential equation","score":0.5571140646934509},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.5011723041534424},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4780060350894928},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.4508976936340332},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.34699928760528564},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07302454113960266},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.06353756785392761}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.8820323944091797},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.820318341255188},{"id":"https://openalex.org/C3445786","wikidata":"https://www.wikidata.org/wiki/Q205805","display_name":"Conservation law","level":2,"score":0.7871387600898743},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.7416922450065613},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.704026997089386},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6389322876930237},{"id":"https://openalex.org/C2780695682","wikidata":"https://www.wikidata.org/wiki/Q4005959","display_name":"Jump","level":2,"score":0.5968598127365112},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5766567587852478},{"id":"https://openalex.org/C111615704","wikidata":"https://www.wikidata.org/wiki/Q2627459","display_name":"Hyperbolic partial differential equation","level":3,"score":0.5571140646934509},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.5011723041534424},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4780060350894928},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.4508976936340332},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.34699928760528564},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07302454113960266},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.06353756785392761},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1137/s106482759833601x","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s106482759833601x","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:discovery.dundee.ac.uk:publications/6cca02ba-9e1d-42a8-b68d-dba3bad80571","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/6cca02ba-9e1d-42a8-b68d-dba3bad80571","pdf_url":"https://discovery.dundee.ac.uk/ws/files/89178/NA180_MAA_DFG_DJH.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aves, M A, Griffiths, D & Higham, D J 2000, 'Runge-Kutta solutions of a hyperbolic conservation law with source term', SIAM Journal on Scientific Computing, vol. 22, no. 1, pp. 20-38. https://doi.org/10.1137/S106482759833601X","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.139.7842","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.139.7842","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.maths.strath.ac.uk/~aas96106/papers/hyp.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.54.6544","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.54.6544","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://homepages.strath.ac.uk/~aas96106/rkhyp.ps.Z","raw_type":"text"},{"id":"pmh:oai:strathprints.strath.ac.uk:179","is_oa":false,"landing_page_url":"https://strathprints.strath.ac.uk/179/","pdf_url":null,"source":{"id":"https://openalex.org/S4306402226","display_name":"Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I181647926","host_organization_name":"University of Strathclyde","host_organization_lineage":["https://openalex.org/I181647926"],"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":"PeerReviewed"}],"best_oa_location":{"id":"pmh:oai:discovery.dundee.ac.uk:publications/6cca02ba-9e1d-42a8-b68d-dba3bad80571","is_oa":true,"landing_page_url":"https://discovery.dundee.ac.uk/en/publications/6cca02ba-9e1d-42a8-b68d-dba3bad80571","pdf_url":"https://discovery.dundee.ac.uk/ws/files/89178/NA180_MAA_DFG_DJH.pdf","source":{"id":"https://openalex.org/S4306400523","display_name":"Discovery Research Portal (University of Dundee)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177639307","host_organization_name":"University of Dundee","host_organization_lineage":["https://openalex.org/I177639307"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Aves, M A, Griffiths, D & Higham, D J 2000, 'Runge-Kutta solutions of a hyperbolic conservation law with source term', SIAM Journal on Scientific Computing, vol. 22, no. 1, pp. 20-38. https://doi.org/10.1137/S106482759833601X","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/15","score":0.6800000071525574,"display_name":"Life in Land"}],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2039558415.pdf","grobid_xml":"https://content.openalex.org/works/W2039558415.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W794663329","https://openalex.org/W1594272372","https://openalex.org/W1974943103","https://openalex.org/W1979352956","https://openalex.org/W1986772166","https://openalex.org/W1991270927","https://openalex.org/W1995673777","https://openalex.org/W1998313971","https://openalex.org/W2043510793","https://openalex.org/W2059340344","https://openalex.org/W2060016579","https://openalex.org/W2067819709","https://openalex.org/W2084265334","https://openalex.org/W2090993472","https://openalex.org/W2094710134","https://openalex.org/W2102662597","https://openalex.org/W2103687696","https://openalex.org/W2117919754","https://openalex.org/W2140291031","https://openalex.org/W2167488568","https://openalex.org/W3003821699","https://openalex.org/W4239883234"],"related_works":["https://openalex.org/W2162899405","https://openalex.org/W3113091479","https://openalex.org/W941090075","https://openalex.org/W2044987316","https://openalex.org/W3134374554","https://openalex.org/W2237480245","https://openalex.org/W2519167559","https://openalex.org/W2075065631","https://openalex.org/W4288358396","https://openalex.org/W4311248832"],"abstract_inverted_index":{"Spurious":[0],"long-term":[1],"solutions":[2,62],"of":[3,36],"a":[4,8,13],"finite-difference":[5],"method":[6],"for":[7,29,47,91],"hyperbolic":[9],"conservation":[10],"law":[11],"with":[12,23,54,63,85],"general":[14,84],"nonlinear":[15,30],"source":[16],"term":[17],"are":[18,21,39],"studied.":[19],"Results":[20],"contrasted":[22],"those":[24],"that":[25,45,56,65,78],"have":[26],"been":[27],"established":[28],"ordinary":[31],"differential":[32],"equations.":[33],"Various":[34],"types":[35],"spurious":[37,79],"behavior":[38,80],"examined,":[40],"including":[41],"spatially":[42],"uniform":[43],"equilibria":[44],"exist":[46,70],"arbitrarily":[48],"small":[49],"time-steps,":[50],"nonsmooth":[51],"steady":[52],"states":[53],"profiles":[55],"jump":[57],"between":[58],"fixed":[59],"levels,":[60],"and":[61,69],"oscillations":[64],"arise":[66],"from":[67],"nonnormality":[68],"only":[71],"in":[72,83,97],"finite":[73],"precision":[74],"arithmetic.":[75],"It":[76],"appears":[77],"is":[81,101],"associated":[82],"insufficient":[86],"spatial":[87],"resolution.":[88],"The":[89],"potential":[90],"curbing":[92],"spuriosity":[93],"by":[94],"using":[95],"adaptivity":[96],"space":[98],"or":[99],"time":[100],"also":[102],"considered.":[103]},"counts_by_year":[{"year":2017,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
