{"id":"https://openalex.org/W1994545070","doi":"https://doi.org/10.1090/s0025-5718-2012-02624-x","title":"Operator splitting for partial differential equations with Burgers nonlinearity","display_name":"Operator splitting for partial differential equations with Burgers nonlinearity","publication_year":2012,"publication_date":"2012-06-12","ids":{"openalex":"https://openalex.org/W1994545070","doi":"https://doi.org/10.1090/s0025-5718-2012-02624-x","mag":"1994545070"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2012-02624-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02624-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02624-X/S0025-5718-2012-02624-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02624-X/S0025-5718-2012-02624-X.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5037337641","display_name":"Helge Holden","orcid":"https://orcid.org/0000-0002-8564-0343"},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]},{"id":"https://openalex.org/I204778367","display_name":"Norwegian University of Science and Technology","ror":"https://ror.org/05xg72x27","country_code":"NO","type":"education","lineage":["https://openalex.org/I204778367"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Helge Holden","raw_affiliation_strings":["Department of Mathematical Sciences, Norwegian University of Science and Technology, NO\u00e2\u0080\u00937491 Trondheim, Norway, \u00e2\u0080\u0094 and \u00e2\u0080\u0094 Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u00e2\u0080\u00930316 Oslo, Norway","Department of Mathematical Sciences, Norwegian University of Science and Technology, NO\u20137491 Trondheim, Norway, and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u20130316 Oslo, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, NO\u00e2\u0080\u00937491 Trondheim, Norway, \u00e2\u0080\u0094 and \u00e2\u0080\u0094 Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u00e2\u0080\u00930316 Oslo, Norway","institution_ids":["https://openalex.org/I184942183","https://openalex.org/I204778367"]},{"raw_affiliation_string":"Department of Mathematical Sciences, Norwegian University of Science and Technology, NO\u20137491 Trondheim, Norway, and Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u20130316 Oslo, Norway","institution_ids":["https://openalex.org/I184942183","https://openalex.org/I204778367"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065792988","display_name":"Christian Lubich","orcid":"https://orcid.org/0000-0003-0105-4927"},"institutions":[{"id":"https://openalex.org/I8087733","display_name":"University of T\u00fcbingen","ror":"https://ror.org/03a1kwz48","country_code":"DE","type":"education","lineage":["https://openalex.org/I8087733"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christian Lubich","raw_affiliation_strings":["Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, D\u00e2\u0080\u009372076 T\u00c3\u00bcbingen, Germany","Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle\u00a010, D-72076 T\u00fcbingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Mathematisches Institut, Universit\u00c3\u00a4t T\u00c3\u00bcbingen, Auf der Morgenstelle 10, D\u00e2\u0080\u009372076 T\u00c3\u00bcbingen, Germany","institution_ids":[]},{"raw_affiliation_string":"Mathematisches Institut, Universit\u00e4t T\u00fcbingen, Auf der Morgenstelle\u00a010, D-72076 T\u00fcbingen, Germany","institution_ids":["https://openalex.org/I8087733"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081764581","display_name":"Nils Henrik Risebro","orcid":"https://orcid.org/0000-0003-4069-8282"},"institutions":[{"id":"https://openalex.org/I184942183","display_name":"University of Oslo","ror":"https://ror.org/01xtthb56","country_code":"NO","type":"education","lineage":["https://openalex.org/I184942183"]}],"countries":["NO"],"is_corresponding":false,"raw_author_name":"Nils Risebro","raw_affiliation_strings":["Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u00e2\u0080\u00930316 Oslo, Norway","Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053, Blindern, NO\u00e2\u0080\u00930316 Oslo, Norway","institution_ids":["https://openalex.org/I184942183"]},{"raw_affiliation_string":"Centre of Mathematics for Applications, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway","institution_ids":["https://openalex.org/I184942183"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":9.2248,"has_fulltext":true,"cited_by_count":97,"citation_normalized_percentile":{"value":0.98968274,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"82","issue":"281","first_page":"173","last_page":"185"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11654","display_name":"Advanced Mathematical Physics Problems","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9980000257492065,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9976999759674072,"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/mathematics","display_name":"Mathematics","score":0.8840926885604858},{"id":"https://openalex.org/keywords/korteweg\u2013de-vries-equation","display_name":"Korteweg\u2013de Vries equation","score":0.8416951894760132},{"id":"https://openalex.org/keywords/burgers-equation","display_name":"Burgers' equation","score":0.693004846572876},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6564533114433289},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.5705500841140747},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.5674488544464111},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5161465406417847},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5011680126190186},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4913844168186188},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4877191483974457},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.46429285407066345},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.07913795113563538},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.052368223667144775}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8840926885604858},{"id":"https://openalex.org/C146630112","wikidata":"https://www.wikidata.org/wiki/Q601796","display_name":"Korteweg\u2013de Vries equation","level":3,"score":0.8416951894760132},{"id":"https://openalex.org/C129747778","wikidata":"https://www.wikidata.org/wiki/Q1014918","display_name":"Burgers' equation","level":3,"score":0.693004846572876},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6564533114433289},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.5705500841140747},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.5674488544464111},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5161465406417847},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5011680126190186},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4913844168186188},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4877191483974457},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.46429285407066345},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.07913795113563538},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.052368223667144775},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-2012-02624-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02624-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02624-X/S0025-5718-2012-02624-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2012-02624-x","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2012-02624-x","pdf_url":"https://www.ams.org/mcom/2013-82-281/S0025-5718-2012-02624-X/S0025-5718-2012-02624-X.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320323299","display_name":"Norges Forskningsr\u00e5d","ror":"https://ror.org/00epmv149"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1994545070.pdf","grobid_xml":"https://content.openalex.org/works/W1994545070.grobid-xml"},"referenced_works_count":22,"referenced_works":["https://openalex.org/W100484353","https://openalex.org/W1487887263","https://openalex.org/W1506032630","https://openalex.org/W1547431580","https://openalex.org/W1559694286","https://openalex.org/W1592378316","https://openalex.org/W1973830399","https://openalex.org/W2009657287","https://openalex.org/W2023174645","https://openalex.org/W2030484509","https://openalex.org/W2042388195","https://openalex.org/W2059691352","https://openalex.org/W2071742362","https://openalex.org/W2072685235","https://openalex.org/W2091470236","https://openalex.org/W2092400970","https://openalex.org/W2150931924","https://openalex.org/W2158738915","https://openalex.org/W2369386221","https://openalex.org/W3209416867","https://openalex.org/W4236581885","https://openalex.org/W4292689972"],"related_works":["https://openalex.org/W2369511497","https://openalex.org/W2319082512","https://openalex.org/W1968180156","https://openalex.org/W2351208265","https://openalex.org/W2048471423","https://openalex.org/W2110627003","https://openalex.org/W2359206539","https://openalex.org/W2368637410","https://openalex.org/W2302683464","https://openalex.org/W2138715427"],"abstract_inverted_index":{"We":[0,97],"provide":[1],"a":[2,68],"new":[3],"analytical":[4],"approach":[5],"to":[6],"operator":[7,71],"splitting":[8,102],"for":[9,118,145],"equations":[10],"of":[11],"the":[12,74,81,85,90,94,100,106,110,119],"type":[13],"<inline-formula":[14,54,127,149,176],"content-type=\"math/mathml\">":[15,55,128,150,177],"<mml:math":[16,56,129,151,178],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[17,57,130,152,179],"alttext=\"u":[18],"Subscript":[19,29],"t":[20],"Baseline":[21],"equals":[22],"upper":[23],"A":[24],"u":[25,27,28],"plus":[26,157],"x\">":[30],"<mml:semantics>":[31,60,135,159,183],"<mml:mrow>":[32,184],"<mml:msub>":[33,42],"<mml:mi>u</mml:mi>":[34,39,41,43],"<mml:mi>t</mml:mi>":[35],"</mml:msub>":[36,45],"<mml:mo>=</mml:mo>":[37],"<mml:mi>A</mml:mi>":[38,61],"<mml:mo>+</mml:mo>":[40,165],"<mml:mi>x</mml:mi>":[44],"</mml:mrow>":[46,167,190],"<mml:annotation":[47,62,140,169,191],"encoding=\"application/x-tex\">u_t=Au+u":[48],"u_x</mml:annotation>":[49],"</mml:semantics>":[50,64,142,171,194],"</mml:math>":[51,65,143,172,195],"</inline-formula>":[52,66,144,173,196],"where":[53],"alttext=\"upper":[58,131,153],"A\">":[59],"encoding=\"application/x-tex\">A</mml:annotation>":[63],"is":[67,76],"linear":[69],"differential":[70],"such":[72],"that":[73,99],"equation":[75,121],"well-posed.":[77],"Particular":[78],"examples":[79],"include":[80],"viscous":[82],"Burgers":[83],"equation,":[84,89,92],"Korteweg\u2013de":[86],"Vries":[87],"(KdV)":[88],"Benney\u2013Lin":[91],"and":[93],"Kawahara":[95],"equation.":[96],"show":[98],"Strang":[101],"method":[103],"converges":[104],"with":[105,174],"expected":[107],"rate":[108],"if":[109],"initial":[111,146],"data":[112,147],"are":[113],"sufficiently":[114],"regular.":[115],"In":[116],"particular,":[117],"KdV":[120],"we":[122],"obtain":[123],"second-order":[124],"convergence":[125],"in":[126,148],"H":[132,154],"Superscript":[133,155],"r\">":[134],"<mml:msup>":[136,160],"<mml:mi>H</mml:mi>":[137,161],"<mml:mi>r</mml:mi>":[138,164,185],"</mml:msup>":[139,168],"encoding=\"application/x-tex\">H^r</mml:annotation>":[141],"r":[156],"5\">":[158],"<mml:mrow":[162],"class=\"MJX-TeXAtom-ORD\">":[163],"<mml:mn>5</mml:mn>":[166],"encoding=\"application/x-tex\">H^{r+5}</mml:annotation>":[170],"arbitrary":[175],"alttext=\"r":[180],"greater-than-or-equal-to":[181],"1\">":[182],"<mml:mo>":[186],"\u2265":[187],"</mml:mo>":[188],"<mml:mn>1</mml:mn>":[189],"encoding=\"application/x-tex\">r\\ge":[192],"1</mml:annotation>":[193],".":[197]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":11},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":11},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":9},{"year":2014,"cited_by_count":5},{"year":2013,"cited_by_count":6},{"year":2012,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
