{"id":"https://openalex.org/W1980621180","doi":"https://doi.org/10.1137/110825789","title":"Stability of Finite Difference Schemes for Complex Diffusion Processes","display_name":"Stability of Finite Difference Schemes for Complex Diffusion Processes","publication_year":2012,"publication_date":"2012-01-01","ids":{"openalex":"https://openalex.org/W1980621180","doi":"https://doi.org/10.1137/110825789","mag":"1980621180"},"language":"en","primary_location":{"id":"doi:10.1137/110825789","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825789","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5052356431","display_name":"Ad\u00e9rito Ara\u00fajo","orcid":"https://orcid.org/0000-0002-9873-5974"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"Ad\u00e9rito Ara\u00fajo","raw_affiliation_strings":["University of Coimbra#TAB#"],"affiliations":[{"raw_affiliation_string":"University of Coimbra#TAB#","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5070343607","display_name":"S\u00edlvia Barbeiro","orcid":"https://orcid.org/0000-0002-2651-5083"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]}],"countries":["PT"],"is_corresponding":false,"raw_author_name":"S\u00edlvia Barbeiro","raw_affiliation_strings":["CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Universidade, 3001-454 Coimbra, Portugal"],"affiliations":[{"raw_affiliation_string":"CMUC, Department of Mathematics, University of Coimbra, Apartado 3008, EC Universidade, 3001-454 Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5003891187","display_name":"Pedro Serranho","orcid":"https://orcid.org/0000-0003-2176-3923"},"institutions":[{"id":"https://openalex.org/I76903346","display_name":"University of Coimbra","ror":"https://ror.org/04z8k9a98","country_code":"PT","type":"education","lineage":["https://openalex.org/I76903346"]},{"id":"https://openalex.org/I201025148","display_name":"Universidade Aberta","ror":"https://ror.org/02rv3w387","country_code":"PT","type":"education","lineage":["https://openalex.org/I201025148"]}],"countries":["PT"],"is_corresponding":true,"raw_author_name":"Pedro Serranho","raw_affiliation_strings":["University of Coimbra, Portugal","Mathematics Section, Department of Science and Technology, Open University, Campus Tagus-Park -Av. Dr. Jacques Delors, 2740-122 Porto Salvo, Oeiras, Portugal and IBILI, Faculty of Medicine,"],"affiliations":[{"raw_affiliation_string":"University of Coimbra, Portugal","institution_ids":["https://openalex.org/I76903346"]},{"raw_affiliation_string":"Mathematics Section, Department of Science and Technology, Open University, Campus Tagus-Park -Av. Dr. Jacques Delors, 2740-122 Porto Salvo, Oeiras, Portugal and IBILI, Faculty of Medicine,","institution_ids":["https://openalex.org/I201025148"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5003891187"],"corresponding_institution_ids":["https://openalex.org/I201025148","https://openalex.org/I76903346"],"apc_list":null,"apc_paid":null,"fwci":3.2946,"has_fulltext":false,"cited_by_count":30,"citation_normalized_percentile":{"value":0.92812988,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"50","issue":"3","first_page":"1284","last_page":"1296"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10052","display_name":"Medical Image Segmentation Techniques","score":0.9970999956130981,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9879000186920166,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7762718200683594},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.6329355835914612},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6231050491333008},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.6153542399406433},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5880883932113647},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.5691605806350708},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5489240288734436},{"id":"https://openalex.org/keywords/image-denoising","display_name":"Image denoising","score":0.5365946292877197},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5327674746513367},{"id":"https://openalex.org/keywords/noise-reduction","display_name":"Noise reduction","score":0.48763003945350647},{"id":"https://openalex.org/keywords/class","display_name":"Class (philosophy)","score":0.4679628312587738},{"id":"https://openalex.org/keywords/diffusion-equation","display_name":"Diffusion equation","score":0.45483630895614624},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.37173646688461304},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32755404710769653},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16212308406829834},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.0916869044303894}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7762718200683594},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6329355835914612},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6231050491333008},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.6153542399406433},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5880883932113647},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.5691605806350708},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5489240288734436},{"id":"https://openalex.org/C2983327147","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Image denoising","level":3,"score":0.5365946292877197},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5327674746513367},{"id":"https://openalex.org/C163294075","wikidata":"https://www.wikidata.org/wiki/Q581861","display_name":"Noise reduction","level":2,"score":0.48763003945350647},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4679628312587738},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.45483630895614624},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.37173646688461304},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32755404710769653},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16212308406829834},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.0916869044303894},{"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/C136264566","wikidata":"https://www.wikidata.org/wiki/Q159810","display_name":"Economy","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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C2780378061","wikidata":"https://www.wikidata.org/wiki/Q25351891","display_name":"Service (business)","level":2,"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:10.1137/110825789","is_oa":false,"landing_page_url":"https://doi.org/10.1137/110825789","pdf_url":null,"source":{"id":"https://openalex.org/S203348814","display_name":"SIAM Journal on Numerical Analysis","issn_l":"0036-1429","issn":["0036-1429","1095-7170"],"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 Numerical Analysis","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.1020.5573","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.1020.5573","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://repositorioaberto.uab.pt///bitstream/10400.2/2176/1/paper_SIAM_rev_last.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1536200267","https://openalex.org/W1591593323","https://openalex.org/W1983078963","https://openalex.org/W2028197830","https://openalex.org/W2058584842","https://openalex.org/W2085202667","https://openalex.org/W2150134853","https://openalex.org/W2156706485","https://openalex.org/W2165015795","https://openalex.org/W2498216762"],"related_works":["https://openalex.org/W2895947835","https://openalex.org/W2087258800","https://openalex.org/W2810018092","https://openalex.org/W2330640442","https://openalex.org/W1975234065","https://openalex.org/W2387428419","https://openalex.org/W2392533133","https://openalex.org/W2617981106","https://openalex.org/W3131191061","https://openalex.org/W2920076344"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3,42],"present":[4,43],"a":[5,12,27,54],"rigorous":[6],"proof":[7],"for":[8],"the":[9,39,58],"stability":[10],"of":[11,14,60],"class":[13],"finite":[15],"difference":[16],"schemes":[17],"applied":[18,52],"to":[19,53],"nonlinear":[20,55],"complex":[21],"diffusion":[22,25],"equations.":[23],"Complex":[24],"is":[26,65],"common":[28],"and":[29],"broadly":[30],"used":[31],"denoising":[32],"procedure":[33],"in":[34,57],"image":[35,61],"processing.":[36],"To":[37],"illustrate":[38],"theoretical":[40],"results":[41],"some":[44],"numerical":[45],"examples":[46],"based":[47],"on":[48],"an":[49],"explicit":[50],"scheme":[51],"equation":[56],"context":[59],"denoising.":[62],"(A":[63],"correction":[64],"attached.)":[66]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":4},{"year":2018,"cited_by_count":2},{"year":2017,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3},{"year":2012,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}