{"id":"https://openalex.org/W4312099809","doi":"https://doi.org/10.1515/cmam-2022-0217","title":"Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity","display_name":"Implicit-Explicit Finite Difference Approximations of a Semilinear Heat Equation with Logarithmic Nonlinearity","publication_year":2023,"publication_date":"2023-03-30","ids":{"openalex":"https://openalex.org/W4312099809","doi":"https://doi.org/10.1515/cmam-2022-0217"},"language":"en","primary_location":{"id":"doi:10.1515/cmam-2022-0217","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0217","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0217/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0217/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010414702","display_name":"Panagiotis Paraschis","orcid":null},"institutions":[{"id":"https://openalex.org/I174458059","display_name":"National Technical University of Athens","ror":"https://ror.org/03cx6bg69","country_code":"GR","type":"education","lineage":["https://openalex.org/I174458059"]}],"countries":["GR"],"is_corresponding":false,"raw_author_name":"Panagiotis Paraschis","raw_affiliation_strings":["School of Applied Mathematical and Physical Sciences , National Technical University of Athens , GR-157 80 Zografou , Greece"],"affiliations":[{"raw_affiliation_string":"School of Applied Mathematical and Physical Sciences , National Technical University of Athens , GR-157 80 Zografou , Greece","institution_ids":["https://openalex.org/I174458059"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5075381508","display_name":"Georgios E. Zouraris","orcid":"https://orcid.org/0000-0003-0234-0175"},"institutions":[{"id":"https://openalex.org/I142617266","display_name":"University of Crete","ror":"https://ror.org/00dr28g20","country_code":"GR","type":"education","lineage":["https://openalex.org/I142617266"]}],"countries":["GR"],"is_corresponding":true,"raw_author_name":"Georgios E. Zouraris","raw_affiliation_strings":["Department of Mathematics and Applied Mathematics , Division of Applied Mathematics: Differential Equations and Numerical Analysis , University of Crete , GR-700 13 Voutes Campus , Heraklion , Crete , Greece"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Applied Mathematics , Division of Applied Mathematics: Differential Equations and Numerical Analysis , University of Crete , GR-700 13 Voutes Campus , Heraklion , Crete , Greece","institution_ids":["https://openalex.org/I142617266"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5075381508"],"corresponding_institution_ids":["https://openalex.org/I142617266"],"apc_list":null,"apc_paid":null,"fwci":0.8238,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.61534501,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"23","issue":"3","first_page":"695","last_page":"713"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9979000091552734,"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":0.9979000091552734,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9962000250816345,"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"}},{"id":"https://openalex.org/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.9955999851226807,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"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":0.5632641911506653},{"id":"https://openalex.org/keywords/logarithm","display_name":"Logarithm","score":0.4816097915172577},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.4660179913043976},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4590209424495697},{"id":"https://openalex.org/keywords/dirichlet-boundary-condition","display_name":"Dirichlet boundary condition","score":0.4397226870059967},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.43373972177505493},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.42944014072418213},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4260683059692383},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4233481287956238},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.39710041880607605},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.39264997839927673},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.3873988091945648}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5632641911506653},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4816097915172577},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.4660179913043976},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4590209424495697},{"id":"https://openalex.org/C110167270","wikidata":"https://www.wikidata.org/wiki/Q1193699","display_name":"Dirichlet boundary condition","level":3,"score":0.4397226870059967},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.43373972177505493},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.42944014072418213},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4260683059692383},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4233481287956238},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.39710041880607605},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.39264997839927673},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.3873988091945648},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","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/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1515/cmam-2022-0217","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0217","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0217/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1515/cmam-2022-0217","is_oa":true,"landing_page_url":"https://doi.org/10.1515/cmam-2022-0217","pdf_url":"https://www.degruyter.com/document/doi/10.1515/cmam-2022-0217/pdf","source":{"id":"https://openalex.org/S2765013998","display_name":"Computational Methods in Applied Mathematics","issn_l":"1609-4840","issn":["1609-4840","1609-9389"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310313990","host_organization_name":"De Gruyter","host_organization_lineage":["https://openalex.org/P4310313990"],"host_organization_lineage_names":["De Gruyter"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational Methods in Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320322644","display_name":"University of Crete","ror":"https://ror.org/00dr28g20"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4312099809.pdf","grobid_xml":"https://content.openalex.org/works/W4312099809.grobid-xml"},"referenced_works_count":21,"referenced_works":["https://openalex.org/W1964889245","https://openalex.org/W1971738560","https://openalex.org/W2032715966","https://openalex.org/W2041278780","https://openalex.org/W2166295771","https://openalex.org/W2610429832","https://openalex.org/W2795033786","https://openalex.org/W2902944228","https://openalex.org/W2904009376","https://openalex.org/W2911671394","https://openalex.org/W2914008319","https://openalex.org/W2962865398","https://openalex.org/W2963738884","https://openalex.org/W3163563819","https://openalex.org/W3210061315","https://openalex.org/W4206791300","https://openalex.org/W4221064267","https://openalex.org/W4224287940","https://openalex.org/W4225769618","https://openalex.org/W4242273588","https://openalex.org/W6743746411"],"related_works":["https://openalex.org/W2122344339","https://openalex.org/W2989780569","https://openalex.org/W2330640442","https://openalex.org/W2466288331","https://openalex.org/W3114093281","https://openalex.org/W1975234065","https://openalex.org/W2145321474","https://openalex.org/W2392533133","https://openalex.org/W4295736060","https://openalex.org/W4220931593"],"abstract_inverted_index":{"Abstract":[0],"We":[1,23],"formulate":[2],"an":[3,62,111],"initial":[4],"and":[5,38,101,195],"Dirichlet":[6],"boundary":[7],"value":[8],"problem":[9],"for":[10,35,49,102,180],"a":[11,19,39,45,146],"semilinear":[12],"heat":[13,188],"equation":[14,189],"with":[15,190],"logarithmic":[16,191],"nonlinearity":[17,192],"over":[18],"two-dimensional":[20],"rectangular":[21],"domain.":[22],"approximate":[24],"its":[25],"solution":[26,185],"by":[27,163],"employing":[28],"the":[29,53,69,103,118,156,159,171,175,181,184,187],"standard":[30],"second-order":[31],"finite":[32,57,106],"difference":[33,58,107],"method":[34,48],"space":[36],"discretization,":[37],"linearized":[40,46,54,104],"backward":[41,55],"Euler":[42,56],"method,":[43,59,108],"or,":[44],"BDF2":[47,105],"time":[50,173],"stepping.":[51],"For":[52],"we":[60,109,154],"derive":[61],"almost":[63,112],"optimal":[64,113],"order":[65,114],"error":[66,115],"estimate":[67,116],"in":[68,117,174],"discrete":[70,119],"<m:math":[71,120],"xmlns:m=\"http://www.w3.org/1998/Math/MathML\">":[72,121],"<m:mrow>":[73,81,122,130],"<m:msubsup>":[74,84,123,133],"<m:mi>L</m:mi>":[75,85,124],"<m:mi>t</m:mi>":[76,125],"<m:mi":[77,87,126],"mathvariant=\"normal\">\u221e</m:mi>":[78,88,127],"</m:msubsup>":[79,89,128,137],"<m:mo>\u2062</m:mo>":[80,129],"<m:mo":[82,90,131,138],"stretchy=\"false\">(</m:mo>":[83,132],"<m:mi>x</m:mi>":[86,135],"stretchy=\"false\">)</m:mo>":[91,139],"</m:mrow>":[92,93,140,141],"</m:math>":[94,142],"L^{\\infty}_{t}(L^{\\infty}_{x})":[95],"-norm":[96],"without":[97],"imposing":[98],"mesh":[99,148],"conditions,":[100],"establish":[110],"<m:mi>H</m:mi>":[134],"<m:mn>1</m:mn>":[136],"L^{\\infty}_{t}(H^{1}_{x})":[143],"-norm,":[144],"allowing":[145],"mild":[147],"condition":[149],"to":[150,186],"be":[151],"satisfied.":[152],"Finally,":[153],"show":[155],"efficiency":[157],"of":[158,183],"numerical":[160,167,178],"methods":[161,179],"proposed,":[162],"exposing":[164],"results":[165],"from":[166],"experiments.":[168],"It":[169],"is":[170],"first":[172],"literature":[176],"where":[177],"approximation":[182],"are":[193],"applied":[194],"analysed.":[196]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
