{"id":"https://openalex.org/W4283814840","doi":"https://doi.org/10.1007/s10915-022-01892-x","title":"Numerical Approximation of a System of Hamilton\u2013Jacobi\u2013Bellman Equations Arising in Innovation Dynamics","display_name":"Numerical Approximation of a System of Hamilton\u2013Jacobi\u2013Bellman Equations Arising in Innovation Dynamics","publication_year":2022,"publication_date":"2022-07-04","ids":{"openalex":"https://openalex.org/W4283814840","doi":"https://doi.org/10.1007/s10915-022-01892-x"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-022-01892-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-01892-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-01892-x.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","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/s10915-022-01892-x.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5091885680","display_name":"\u013dubom\u00edr Ba\u0148as","orcid":"https://orcid.org/0000-0003-3041-6405"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"L\u2019ubom\u00edr Ba\u0148as","raw_affiliation_strings":["Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany"],"raw_orcid":"https://orcid.org/0000-0003-3041-6405","affiliations":[{"raw_affiliation_string":"Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043134112","display_name":"Herbert Dawid","orcid":"https://orcid.org/0000-0002-8536-9960"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I203082224","display_name":"Hochschule Bielefeld","ror":"https://ror.org/00edvg943","country_code":"DE","type":"education","lineage":["https://openalex.org/I203082224"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Herbert Dawid","raw_affiliation_strings":["Bielefeld University, Faculty of Business Administration and Economics, Universittsstr 25, DE 33615 Bielefeld, Germany","Bielefeld University, Faculty of Business Administration and Economics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bielefeld University, Faculty of Business Administration and Economics, Universittsstr 25, DE 33615 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455","https://openalex.org/I203082224"]},{"raw_affiliation_string":"Bielefeld University, Faculty of Business Administration and Economics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011170260","display_name":"Tsiry Avisoa Randrianasolo","orcid":"https://orcid.org/0000-0002-9413-5189"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Tsiry Avisoa Randrianasolo","raw_affiliation_strings":["Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089019825","display_name":"Johannes Storn","orcid":"https://orcid.org/0000-0003-1520-6557"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I203082224","display_name":"Hochschule Bielefeld","ror":"https://ror.org/00edvg943","country_code":"DE","type":"education","lineage":["https://openalex.org/I203082224"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Johannes Storn","raw_affiliation_strings":["Bielefeld University, Faculty of Mathematics, Universittsstr 25, DE 33615 Bielefeld, Germany","Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bielefeld University, Faculty of Mathematics, Universittsstr 25, DE 33615 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455","https://openalex.org/I203082224"]},{"raw_affiliation_string":"Bielefeld University, Faculty of Mathematics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5079961142","display_name":"Xingang Wen","orcid":"https://orcid.org/0000-0001-5410-7434"},"institutions":[{"id":"https://openalex.org/I20121455","display_name":"Bielefeld University","ror":"https://ror.org/02hpadn98","country_code":"DE","type":"education","lineage":["https://openalex.org/I20121455"]},{"id":"https://openalex.org/I203082224","display_name":"Hochschule Bielefeld","ror":"https://ror.org/00edvg943","country_code":"DE","type":"education","lineage":["https://openalex.org/I203082224"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Xingang Wen","raw_affiliation_strings":["Bielefeld University, Faculty of Business Administration and Economics, Universittsstr 25, DE 33615 Bielefeld, Germany","Bielefeld University, Faculty of Business Administration and Economics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bielefeld University, Faculty of Business Administration and Economics, Universittsstr 25, DE 33615 Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455","https://openalex.org/I203082224"]},{"raw_affiliation_string":"Bielefeld University, Faculty of Business Administration and Economics, Universit\u00e4tsstr 25, DE 33615, Bielefeld, Germany","institution_ids":["https://openalex.org/I20121455"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5091885680"],"corresponding_institution_ids":["https://openalex.org/I20121455"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":{"value":2390,"currency":"EUR","value_usd":2990},"fwci":0.6286,"has_fulltext":true,"cited_by_count":4,"citation_normalized_percentile":{"value":0.69662466,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"92","issue":"2","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10067","display_name":"Stochastic processes and financial applications","score":0.9948999881744385,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9940000176429749,"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/T10360","display_name":"Fluid Dynamics and Turbulent Flows","score":0.991100013256073,"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":0.7604449987411499},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5915849804878235},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi-equation","display_name":"Hamilton\u2013Jacobi equation","score":0.5865439176559448},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.5274118185043335},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.5082668662071228},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4893607497215271},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4636237621307373},{"id":"https://openalex.org/keywords/bellman-equation","display_name":"Bellman equation","score":0.4573464095592499},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.44017618894577026},{"id":"https://openalex.org/keywords/hamilton\u2013jacobi\u2013bellman-equation","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","score":0.43075382709503174},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34258896112442017},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.32058221101760864},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.31426507234573364},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.29430150985717773},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1395396888256073}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7604449987411499},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5915849804878235},{"id":"https://openalex.org/C2778860007","wikidata":"https://www.wikidata.org/wiki/Q1060137","display_name":"Hamilton\u2013Jacobi equation","level":2,"score":0.5865439176559448},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.5274118185043335},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5082668662071228},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4893607497215271},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4636237621307373},{"id":"https://openalex.org/C14646407","wikidata":"https://www.wikidata.org/wiki/Q1430750","display_name":"Bellman equation","level":2,"score":0.4573464095592499},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.44017618894577026},{"id":"https://openalex.org/C196978813","wikidata":"https://www.wikidata.org/wiki/Q3302775","display_name":"Hamilton\u2013Jacobi\u2013Bellman equation","level":3,"score":0.43075382709503174},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34258896112442017},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32058221101760864},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.31426507234573364},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.29430150985717773},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1395396888256073},{"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/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1007/s10915-022-01892-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-01892-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-01892-x.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},{"id":"pmh:oai:pub.uni-bielefeld.de:2964034","is_oa":true,"landing_page_url":"https://pub.uni-bielefeld.de/record/2964034","pdf_url":null,"source":{"id":"https://openalex.org/S4306401670","display_name":"PUB \u2013 Publications at Bielefeld University (Bielefeld University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I20121455","host_organization_name":"Bielefeld University","host_organization_lineage":["https://openalex.org/I20121455"],"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":"http://purl.org/coar/resource_type/c_6501"}],"best_oa_location":{"id":"doi:10.1007/s10915-022-01892-x","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s10915-022-01892-x","pdf_url":"https://link.springer.com/content/pdf/10.1007/s10915-022-01892-x.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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Industry, innovation and infrastructure","id":"https://metadata.un.org/sdg/9","score":0.6700000166893005}],"awards":[{"id":"https://openalex.org/G3726739138","display_name":null,"funder_award_id":"SFB 1283/2 2021-317210226","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G6538932988","display_name":null,"funder_award_id":"SFB 1283","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G7804956510","display_name":null,"funder_award_id":"2021-317210226","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8201362140","display_name":null,"funder_award_id":"SFB 1283/2 2021","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"},{"id":"https://openalex.org/G8439510294","display_name":null,"funder_award_id":"317210226","funder_id":"https://openalex.org/F4320320879","funder_display_name":"Deutsche Forschungsgemeinschaft"}],"funders":[{"id":"https://openalex.org/F4320320879","display_name":"Deutsche Forschungsgemeinschaft","ror":"https://ror.org/018mejw64"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4283814840.pdf","grobid_xml":"https://content.openalex.org/works/W4283814840.grobid-xml"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W61439753","https://openalex.org/W592962635","https://openalex.org/W1507126399","https://openalex.org/W1529207392","https://openalex.org/W1974834572","https://openalex.org/W1974854353","https://openalex.org/W1983195644","https://openalex.org/W1985843599","https://openalex.org/W1993281803","https://openalex.org/W1996308226","https://openalex.org/W1998360780","https://openalex.org/W2005448420","https://openalex.org/W2015119017","https://openalex.org/W2017827790","https://openalex.org/W2021092589","https://openalex.org/W2024969615","https://openalex.org/W2039150507","https://openalex.org/W2045849310","https://openalex.org/W2088299544","https://openalex.org/W2093711514","https://openalex.org/W2127061658","https://openalex.org/W2157494358","https://openalex.org/W2169143985","https://openalex.org/W2177195156","https://openalex.org/W2923537224","https://openalex.org/W2963243433","https://openalex.org/W2963701079","https://openalex.org/W3098321018","https://openalex.org/W3099267538","https://openalex.org/W3106017595","https://openalex.org/W4245654886","https://openalex.org/W4255975175"],"related_works":["https://openalex.org/W2032834442","https://openalex.org/W3153900688","https://openalex.org/W2115544975","https://openalex.org/W2902017027","https://openalex.org/W1914731323","https://openalex.org/W1654696814","https://openalex.org/W4291598237","https://openalex.org/W4239477580","https://openalex.org/W4226406511","https://openalex.org/W1996904445"],"abstract_inverted_index":{"Abstract":[0],"We":[1,34,61],"consider":[2],"a":[3,28],"system":[4],"of":[5,21,27,42],"fully":[6],"nonlinear":[7],"partial":[8],"differential":[9],"equations":[10,16],"that":[11],"corresponds":[12],"to":[13,77],"the":[14,18,39,43,46,49,56,66],"Hamilton\u2013Jacobi\u2013Bellman":[15],"for":[17,38,65,73],"value":[19],"functions":[20],"an":[22],"optimal":[23],"innovation":[24],"investment":[25],"problem":[26],"monopoly":[29],"firm":[30],"facing":[31],"bankruptcy":[32],"risk.":[33],"compare":[35],"several":[36],"algorithms":[37],"numerical":[40,71],"solution":[41],"considered":[44,67],"problem:":[45],"collocation":[47],"method,":[48,52],"finite":[50,58],"difference":[51],"WENO":[53],"method":[54],"and":[55,69],"adaptive":[57],"element":[59],"method.":[60],"discuss":[62],"implementation":[63],"issues":[64],"schemes":[68],"perform":[70],"studies":[72],"different":[74],"model":[75],"parameters":[76],"assess":[78],"their":[79],"performance.":[80]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}