{"id":"https://openalex.org/W2337453864","doi":"https://doi.org/10.1007/s11075-016-0206-8","title":"Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions","display_name":"Adaptive high-order splitting methods for systems of nonlinear evolution equations with periodic boundary conditions","publication_year":2016,"publication_date":"2016-10-03","ids":{"openalex":"https://openalex.org/W2337453864","doi":"https://doi.org/10.1007/s11075-016-0206-8","mag":"2337453864"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-016-0206-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-016-0206-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11075-016-0206-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007%2Fs11075-016-0206-8.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5078223437","display_name":"Winfried Auzinger","orcid":"https://orcid.org/0000-0002-9631-2601"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":true,"raw_author_name":"Winfried Auzinger","raw_affiliation_strings":["Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/E101, 1040, Wien, Austria","Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wien, Austria 1040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/E101, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wien, Austria 1040#TAB#","institution_ids":["https://openalex.org/I145847075"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056549733","display_name":"Othmar Koch","orcid":"https://orcid.org/0000-0002-1956-221X"},"institutions":[{"id":"https://openalex.org/I129774422","display_name":"University of Vienna","ror":"https://ror.org/03prydq77","country_code":"AT","type":"education","lineage":["https://openalex.org/I129774422"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Othmar Koch","raw_affiliation_strings":["Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Wien, Austria 1090#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Oskar-Morgenstern-Platz 1, 1090, Wien, Austria","institution_ids":["https://openalex.org/I129774422"]},{"raw_affiliation_string":"Fakult\u00e4t f\u00fcr Mathematik, Universit\u00e4t Wien, Wien, Austria 1090#TAB#","institution_ids":["https://openalex.org/I129774422"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5027848130","display_name":"Michael Quell","orcid":"https://orcid.org/0000-0002-4787-152X"},"institutions":[{"id":"https://openalex.org/I145847075","display_name":"TU Wien","ror":"https://ror.org/04d836q62","country_code":"AT","type":"education","lineage":["https://openalex.org/I145847075"]}],"countries":["AT"],"is_corresponding":false,"raw_author_name":"Michael Quell","raw_affiliation_strings":["Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/E101, 1040, Wien, Austria","Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wien, Austria 1040#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wiedner Hauptstra\u00dfe 8-10/E101, 1040, Wien, Austria","institution_ids":["https://openalex.org/I145847075"]},{"raw_affiliation_string":"Institut f\u00fcr Analysis und Scientific Computing, Technische Universit\u00e4t Wien, Wien, Austria 1040#TAB#","institution_ids":["https://openalex.org/I145847075"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078223437"],"corresponding_institution_ids":["https://openalex.org/I145847075"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":{"value":2990,"currency":"USD","value_usd":2990},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04314293,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"75","issue":"1","first_page":"261","last_page":"283"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9994999766349792,"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/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9988999962806702,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9987000226974487,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6456665992736816},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6397859454154968},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.6064682006835938},{"id":"https://openalex.org/keywords/a-priori-and-a-posteriori","display_name":"A priori and a posteriori","score":0.5646722316741943},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5407407879829407},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5189375877380371},{"id":"https://openalex.org/keywords/periodic-boundary-conditions","display_name":"Periodic boundary conditions","score":0.4810605049133301},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.4634964168071747},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4554142951965332},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.44197404384613037},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38525834679603577},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.2559239864349365},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06854918599128723}],"concepts":[{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6456665992736816},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6397859454154968},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.6064682006835938},{"id":"https://openalex.org/C75553542","wikidata":"https://www.wikidata.org/wiki/Q178161","display_name":"A priori and a posteriori","level":2,"score":0.5646722316741943},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5407407879829407},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5189375877380371},{"id":"https://openalex.org/C112675119","wikidata":"https://www.wikidata.org/wiki/Q2992284","display_name":"Periodic boundary conditions","level":3,"score":0.4810605049133301},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4634964168071747},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4554142951965332},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.44197404384613037},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38525834679603577},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2559239864349365},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06854918599128723},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1007/s11075-016-0206-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-016-0206-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11075-016-0206-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1604.01201","is_oa":true,"landing_page_url":"https://arxiv.org/abs/1604.01201","pdf_url":"https://arxiv.org/pdf/1604.01201","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":null,"raw_type":"text"},{"id":"mag:2337453864","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1604.01201.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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:repositum.tuwien.ac.at:1746053","is_oa":true,"landing_page_url":"http://resolver.obvsg.at/urn:nbn:at:at-ubtuw:3-2830","pdf_url":null,"source":{"id":"https://openalex.org/S4306400493","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"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":"Text"},{"id":"pmh:oai:repositum.tuwien.at:20.500.12708/336","is_oa":true,"landing_page_url":"http://hdl.handle.net/20.500.12708/336","pdf_url":null,"source":{"id":"https://openalex.org/S4306400493","display_name":"reposiTUm (TU Wien)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I145847075","host_organization_name":"TU Wien","host_organization_lineage":["https://openalex.org/I145847075"],"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.1604.01201","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1604.01201","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"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":"Preprint"}],"best_oa_location":{"id":"doi:10.1007/s11075-016-0206-8","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11075-016-0206-8","pdf_url":"https://link.springer.com/content/pdf/10.1007%2Fs11075-016-0206-8.pdf","source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"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":"Numerical Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1280300241","display_name":"Adaptive Splitting for Nonlinear Schr\u00f6dinger Equations","funder_award_id":"P 24157","funder_id":"https://openalex.org/F4320321181","funder_display_name":"Austrian Science Fund"},{"id":"https://openalex.org/G5421925520","display_name":"Adaptive Time-Splitting for Many-Body Quantum Propagation","funder_award_id":"MA14-002","funder_id":"https://openalex.org/F4320321003","funder_display_name":"Vienna Science and Technology Fund"}],"funders":[{"id":"https://openalex.org/F4320321003","display_name":"Vienna Science and Technology Fund","ror":"https://ror.org/01f9mc681"},{"id":"https://openalex.org/F4320321181","display_name":"Austrian Science Fund","ror":"https://ror.org/013tf3c58"},{"id":"https://openalex.org/F4320324717","display_name":"Tartu \u00dclikool","ror":"https://ror.org/03z77qz90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2337453864.pdf","grobid_xml":"https://content.openalex.org/works/W2337453864.grobid-xml"},"referenced_works_count":28,"referenced_works":["https://openalex.org/W1592378316","https://openalex.org/W1594563152","https://openalex.org/W1594927479","https://openalex.org/W1884654681","https://openalex.org/W1967084062","https://openalex.org/W1967159254","https://openalex.org/W1973102985","https://openalex.org/W2014289408","https://openalex.org/W2015922651","https://openalex.org/W2049161806","https://openalex.org/W2050545584","https://openalex.org/W2051494558","https://openalex.org/W2055178055","https://openalex.org/W2058066520","https://openalex.org/W2060343045","https://openalex.org/W2074376958","https://openalex.org/W2082390516","https://openalex.org/W2092400970","https://openalex.org/W2095610153","https://openalex.org/W2114363690","https://openalex.org/W2118085053","https://openalex.org/W2142885234","https://openalex.org/W2185319997","https://openalex.org/W2336570447","https://openalex.org/W2947056241","https://openalex.org/W3020873732","https://openalex.org/W3209416867","https://openalex.org/W4211077197"],"related_works":["https://openalex.org/W2964252389","https://openalex.org/W3087589158","https://openalex.org/W3088272677","https://openalex.org/W3039764731","https://openalex.org/W3173856472","https://openalex.org/W3049614092","https://openalex.org/W631488808","https://openalex.org/W3101363733","https://openalex.org/W2807523282","https://openalex.org/W2127650438","https://openalex.org/W3158980235","https://openalex.org/W2950564506","https://openalex.org/W1973303223","https://openalex.org/W3111337353","https://openalex.org/W3171753014","https://openalex.org/W1621188459","https://openalex.org/W2185816199","https://openalex.org/W172668505","https://openalex.org/W3047922823","https://openalex.org/W3206478649"],"abstract_inverted_index":{"We":[0,26],"assess":[1],"the":[2,13,59,64,70,74,82,85,91],"applicability":[3],"and":[4,35,57,73,87,98],"efficiency":[5,92],"of":[6,16,84,93,99],"time-adaptive":[7,95],"high-order":[8],"splitting":[9,48,96,100],"methods":[10,49,86],"applied":[11],"for":[12,47,50,69],"numerical":[14],"solution":[15,38,66],"(systems":[17],"of)":[18],"nonlinear":[19],"parabolic":[20,51],"problems":[21,52],"under":[22,53],"periodic":[23,54],"boundary":[24,55],"conditions.":[25],"discuss":[27],"in":[28,67],"particular":[29,68],"several":[30],"applications":[31],"generating":[32],"intricate":[33],"patterns":[34],"displaying":[36],"nonsmooth":[37],"dynamics.":[39],"First,":[40],"we":[41],"give":[42],"a":[43,111],"general":[44],"error":[45,114],"analysis":[46],"conditions":[56],"derive":[58],"necessary":[60],"smoothness":[61],"requirements":[62],"on":[63,108],"exact":[65],"Gray\u2013Scott":[71],"equation":[72],"Van":[75],"der":[76],"Pol":[77],"equation.":[78],"Numerical":[79],"examples":[80],"demonstrate":[81],"convergence":[83],"serve":[88],"to":[89],"compare":[90],"different":[94],"schemes":[97],"into":[101],"either":[102],"two":[103],"or":[104],"three":[105],"operators,":[106],"based":[107],"appropriately":[109],"constructed":[110],"posteriori":[112],"local":[113],"estimators.":[115]},"counts_by_year":[],"updated_date":"2026-08-14T07:06:38.338062","created_date":"2025-10-10T00:00:00"}