{"id":"https://openalex.org/W3126295154","doi":"https://doi.org/10.1007/s10915-021-01454-7","title":"A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions","display_name":"A New Class of A Stable Summation by Parts Time Integration Schemes with Strong Initial Conditions","publication_year":2021,"publication_date":"2021-03-10","ids":{"openalex":"https://openalex.org/W3126295154","doi":"https://doi.org/10.1007/s10915-021-01454-7","mag":"3126295154"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01454-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01454-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01454-7.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":"preprint","indexed_in":["crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01454-7.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5056123559","display_name":"Hendrik Ranocha","orcid":"https://orcid.org/0000-0002-3456-2277"},"institutions":[{"id":"https://openalex.org/I22465464","display_name":"University of M\u00fcnster","ror":"https://ror.org/00pd74e08","country_code":"DE","type":"education","lineage":["https://openalex.org/I22465464"]},{"id":"https://openalex.org/I71920554","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38","country_code":"SA","type":"education","lineage":["https://openalex.org/I71920554"]}],"countries":["DE","SA"],"is_corresponding":true,"raw_author_name":"Hendrik Ranocha","raw_affiliation_strings":["Computer Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia","Mathematics M\u00fcnster, University of M\u00fcnster, M\u00fcnster, Germany","Computer Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia"],"affiliations":[{"raw_affiliation_string":"Computer Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal 23955-6900, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]},{"raw_affiliation_string":"Mathematics M\u00fcnster, University of M\u00fcnster, M\u00fcnster, Germany","institution_ids":["https://openalex.org/I22465464"]},{"raw_affiliation_string":"Computer Electrical and Mathematical Science and Engineering Division (CEMSE), King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia","institution_ids":["https://openalex.org/I71920554"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057106073","display_name":"Jan Nordstr\u00f6m","orcid":"https://orcid.org/0000-0002-7972-6183"},"institutions":[{"id":"https://openalex.org/I102134673","display_name":"Link\u00f6ping University","ror":"https://ror.org/05ynxx418","country_code":"SE","type":"education","lineage":["https://openalex.org/I102134673"]},{"id":"https://openalex.org/I24027795","display_name":"University of Johannesburg","ror":"https://ror.org/04z6c2n17","country_code":"ZA","type":"education","lineage":["https://openalex.org/I24027795"]}],"countries":["SE","ZA"],"is_corresponding":false,"raw_author_name":"Jan Nordstr\u00f6m","raw_affiliation_strings":["Department of Mathematics, Applied Mathematics, Link\u00f6ping University, Link\u00f6ping, Sweden","Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Applied Mathematics, Link\u00f6ping University, Link\u00f6ping, Sweden","institution_ids":["https://openalex.org/I102134673"]},{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics, University of Johannesburg, Johannesburg, South Africa","institution_ids":["https://openalex.org/I24027795"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5056123559"],"corresponding_institution_ids":["https://openalex.org/I22465464","https://openalex.org/I71920554"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.0319339,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":96},"biblio":{"volume":"87","issue":"1","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":0.9998999834060669,"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":0.9998999834060669,"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":0.9965999722480774,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9958999752998352,"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/collocation","display_name":"Collocation (remote sensing)","score":0.6664072871208191},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6292755007743835},{"id":"https://openalex.org/keywords/summation-by-parts","display_name":"Summation by parts","score":0.6245030760765076},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6194901466369629},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.5973356366157532},{"id":"https://openalex.org/keywords/projection","display_name":"Projection (relational algebra)","score":0.5441537499427795},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5397554039955139},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.535927951335907},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5145825743675232},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.48666125535964966},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.4684322774410248},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4626205265522003},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.4577445387840271},{"id":"https://openalex.org/keywords/projection-method","display_name":"Projection method","score":0.43187665939331055},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.4164988100528717},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.38679084181785583},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.31458765268325806},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.30991411209106445},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.29358363151550293},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.2083207666873932},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.1515693962574005},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11782637238502502},{"id":"https://openalex.org/keywords/dykstras-projection-algorithm","display_name":"Dykstra's projection algorithm","score":0.0894274115562439}],"concepts":[{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6664072871208191},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6292755007743835},{"id":"https://openalex.org/C13626590","wikidata":"https://www.wikidata.org/wiki/Q318754","display_name":"Summation by parts","level":2,"score":0.6245030760765076},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6194901466369629},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.5973356366157532},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.5441537499427795},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5397554039955139},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.535927951335907},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5145825743675232},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.48666125535964966},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.4684322774410248},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4626205265522003},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.4577445387840271},{"id":"https://openalex.org/C65557600","wikidata":"https://www.wikidata.org/wiki/Q7249451","display_name":"Projection method","level":3,"score":0.43187665939331055},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.4164988100528717},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.38679084181785583},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.31458765268325806},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30991411209106445},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.29358363151550293},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2083207666873932},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.1515693962574005},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11782637238502502},{"id":"https://openalex.org/C202426404","wikidata":"https://www.wikidata.org/wiki/Q5318686","display_name":"Dykstra's projection algorithm","level":2,"score":0.0894274115562439},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1007/s10915-021-01454-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01454-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01454-7.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":"mag:3126295154","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2003.03889.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"pmh:oai:DiVA.org:liu-173945","is_oa":true,"landing_page_url":"http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-173945","pdf_url":null,"source":{"id":"https://openalex.org/S4306401559","display_name":"KTH Publication Database DiVA (KTH Royal Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article in journal"},{"id":"pmh:oai:repository.kaust.edu.sa:10754/662303","is_oa":true,"landing_page_url":"http://hdl.handle.net/10754/662303","pdf_url":null,"source":{"id":"https://openalex.org/S4306401596","display_name":"King Abdullah University of Science and Technology Repository (King Abdullah 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/I71920554","host_organization_name":"King Abdullah University of Science and Technology","host_organization_lineage":["https://openalex.org/I71920554"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"doi:10.48550/arxiv.2003.03889","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2003.03889","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.1007/s10915-021-01454-7","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-021-01454-7","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-021-01454-7.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":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.8399999737739563}],"awards":[{"id":"https://openalex.org/G2826949580","display_name":null,"funder_award_id":"SESSI","funder_id":"https://openalex.org/F4320317161","funder_display_name":"Swedish e-Science Research Centre"},{"id":"https://openalex.org/G3814625421","display_name":null,"funder_award_id":"2018-05084","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G429956873","display_name":null,"funder_award_id":"2018-05084_VR","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G712881263","display_name":null,"funder_award_id":"2018-","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G7228997265","display_name":null,"funder_award_id":"Vetenskapsr\u00e5","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"},{"id":"https://openalex.org/G7790445587","display_name":null,"funder_award_id":"2018-05084 VR","funder_id":"https://openalex.org/F4320322581","funder_display_name":"Vetenskapsr\u00e5det"}],"funders":[{"id":"https://openalex.org/F4320317161","display_name":"Swedish e-Science Research Centre","ror":"https://ror.org/01e59yk92"},{"id":"https://openalex.org/F4320322225","display_name":"Link\u00f6pings Universitet","ror":"https://ror.org/05ynxx418"},{"id":"https://openalex.org/F4320322320","display_name":"King Abdullah University of Science and Technology","ror":"https://ror.org/01q3tbs38"},{"id":"https://openalex.org/F4320322581","display_name":"Vetenskapsr\u00e5det","ror":"https://ror.org/03zttf063"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3126295154.pdf","grobid_xml":"https://content.openalex.org/works/W3126295154.grobid-xml"},"referenced_works_count":54,"referenced_works":["https://openalex.org/W96454744","https://openalex.org/W1543750907","https://openalex.org/W1965855805","https://openalex.org/W1972670182","https://openalex.org/W1976349874","https://openalex.org/W1978362527","https://openalex.org/W1989955731","https://openalex.org/W1995071315","https://openalex.org/W2004759358","https://openalex.org/W2007169649","https://openalex.org/W2010049741","https://openalex.org/W2011301426","https://openalex.org/W2013404213","https://openalex.org/W2022981527","https://openalex.org/W2042388195","https://openalex.org/W2043341868","https://openalex.org/W2049068370","https://openalex.org/W2049991352","https://openalex.org/W2051465806","https://openalex.org/W2065978762","https://openalex.org/W2117243944","https://openalex.org/W2120575449","https://openalex.org/W2176519845","https://openalex.org/W2265668744","https://openalex.org/W2743040688","https://openalex.org/W2753944674","https://openalex.org/W2765460213","https://openalex.org/W2794020691","https://openalex.org/W2809148218","https://openalex.org/W2810109327","https://openalex.org/W2902291819","https://openalex.org/W2902420577","https://openalex.org/W2911611941","https://openalex.org/W2945076242","https://openalex.org/W2966767209","https://openalex.org/W2969452854","https://openalex.org/W2975923947","https://openalex.org/W2976777265","https://openalex.org/W2995756203","https://openalex.org/W2998555047","https://openalex.org/W2999948526","https://openalex.org/W3009636994","https://openalex.org/W3011239099","https://openalex.org/W3039534546","https://openalex.org/W3096719680","https://openalex.org/W3103244101","https://openalex.org/W3106538085","https://openalex.org/W3109800837","https://openalex.org/W3110634721","https://openalex.org/W3134568949","https://openalex.org/W4234402868","https://openalex.org/W4240530219","https://openalex.org/W4293163450","https://openalex.org/W6893667455"],"related_works":["https://openalex.org/W2090361314","https://openalex.org/W1539245580","https://openalex.org/W2047183951","https://openalex.org/W1742927704","https://openalex.org/W2795045700","https://openalex.org/W2742559260","https://openalex.org/W3197979304","https://openalex.org/W1977062482","https://openalex.org/W2171701494","https://openalex.org/W2962762212","https://openalex.org/W947168642","https://openalex.org/W2127382446","https://openalex.org/W1974878687","https://openalex.org/W2045244586","https://openalex.org/W2224576969","https://openalex.org/W2892577216","https://openalex.org/W2625818144","https://openalex.org/W2006530190","https://openalex.org/W2736744674"],"abstract_inverted_index":{"Abstract":[0],"Since":[1],"integration":[2,53,70],"by":[3,26,43],"parts":[4,27],"is":[5,30,131],"an":[6,116],"important":[7],"tool":[8],"when":[9],"deriving":[10],"energy":[11],"or":[12],"entropy":[13],"estimates":[14],"for":[15],"differential":[16],"equations,":[17],"one":[18],"may":[19],"conjecture":[20],"that":[21],"some":[22],"form":[23],"of":[24,48,103],"summation":[25],"(SBP)":[28],"property":[29],"involved":[31],"in":[32],"provably":[33],"stable":[34,50],"numerical":[35],"methods.":[36,63],"This":[37],"article":[38],"contributes":[39],"to":[40,66,76,89],"this":[41],"topic":[42],"proposing":[44],"a":[45,86,120],"novel":[46],"class":[47,102],"A":[49],"SBP":[51,68,98,117,122],"time":[52,69],"methods":[54,71,104],"which":[55],"can":[56],"also":[57],"be":[58],"reformulated":[59],"as":[60,115],"implicit":[61],"Runge-Kutta":[62],"In":[64],"contrast":[65],"existing":[67],"using":[72],"simultaneous":[73],"approximation":[74],"terms":[75],"impose":[77,90],"the":[78,82,91,97,106,125],"initial":[79,92],"condition":[80,93],"weakly,":[81],"new":[83,101],"schemes":[84],"use":[85],"projection":[87],"method":[88,130],"strongly":[94],"without":[95],"destroying":[96],"property.":[99],"The":[100],"includes":[105],"classical":[107,126],"Lobatto":[108,127],"IIIA":[109],"collocation":[110,129],"method,":[111],"not":[112],"previously":[113],"formulated":[114],"scheme.":[118],"Additionally,":[119],"related":[121],"scheme":[123],"including":[124],"IIIB":[128],"developed.":[132]},"counts_by_year":[{"year":2020,"cited_by_count":2}],"updated_date":"2026-04-14T08:04:32.555800","created_date":"2025-10-10T00:00:00"}
