{"id":"https://openalex.org/W7167089881","doi":"https://doi.org/10.48550/arxiv.2607.00489","title":"A Nonstandard Finite Difference Scheme for a Nonlinear Parabolic Equation with p-Laplacian-Type Diffusion","display_name":"A Nonstandard Finite Difference Scheme for a Nonlinear Parabolic Equation with p-Laplacian-Type Diffusion","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167089881","doi":"https://doi.org/10.48550/arxiv.2607.00489"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.00489","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092681517","display_name":"Achraf Zinihi","orcid":"https://orcid.org/0009-0001-3245-2779"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zinihi, Achraf","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139920406","display_name":"Matthias Ehrhardt","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ehrhardt, Matthias","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5083135232","display_name":"Moulay Rchid Sidi Ammi","orcid":"https://orcid.org/0000-0002-4488-9070"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ammi, Moulay Rchid Sidi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12589","display_name":"Differential Equations and Boundary Problems","score":0.2298000007867813,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.2298000007867813,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T10194","display_name":"Nonlinear Partial Differential Equations","score":0.13750000298023224,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T11110","display_name":"Stability and Controllability of Differential Equations","score":0.08900000154972076,"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/nonlinear-system","display_name":"Nonlinear system","score":0.6865000128746033},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6460999846458435},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5324000120162964},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.5242000222206116},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.5184000134468079},{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.5055000185966492},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.48510000109672546},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46700000762939453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7524999976158142},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6865000128746033},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6460999846458435},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5751000046730042},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5324000120162964},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.5242000222206116},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.5184000134468079},{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.5055000185966492},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.48510000109672546},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46700000762939453},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4124000072479248},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.40689998865127563},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3815999925136566},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3767000138759613},{"id":"https://openalex.org/C2780829570","wikidata":"https://www.wikidata.org/wiki/Q25113057","display_name":"Compact finite difference","level":3,"score":0.36340001225471497},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.3621000051498413},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.3188999891281128},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.2946000099182129},{"id":"https://openalex.org/C202787564","wikidata":"https://www.wikidata.org/wiki/Q6510488","display_name":"Heat equation","level":2,"score":0.26980000734329224},{"id":"https://openalex.org/C108268861","wikidata":"https://www.wikidata.org/wiki/Q1747602","display_name":"Finite difference coefficient","level":4,"score":0.2678000032901764},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.26759999990463257}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.00489","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00489","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"We":[0,82],"propose":[1],"and":[2,21,70,94,99,109,124],"analyze":[3],"a":[4,15,33,40,50],"nonstandard":[5],"finite":[6,78],"difference":[7,79],"(NSFD)":[8],"scheme":[9,55,120],"for":[10,129],"nonlinear":[11,34,45],"parabolic":[12],"equations":[13],"involving":[14],"p-Laplacian-type":[16],"diffusion":[17,46],"operator":[18],"in":[19],"one-":[20],"two-dimensional":[22],"spatial":[23],"domains.":[24],"Following":[25],"Mickens'":[26],"design":[27],"principles,":[28],"the":[29,44,64,84,87,91,106,113,117],"proposed":[30,118],"discretization":[31],"employs":[32],"denominator":[35],"function":[36],"phi(.)":[37],"together":[38],"with":[39],"nonlocal":[41],"approximation":[42],"of":[43,63,86],"term":[47],"Delta_p,":[48],"yielding":[49],"structure-preserving":[51],"discrete":[52],"model.":[53],"The":[54],"is":[56],"designed":[57],"to":[58],"retain":[59],"key":[60],"qualitative":[61],"properties":[62],"continuous":[65,88],"problem,":[66],"including":[67],"positivity,":[68],"boundedness,":[69],"stability,":[71],"which":[72],"may":[73],"be":[74],"lost":[75],"by":[76],"standard":[77,114],"methods":[80],"(FDMs).":[81],"establish":[83],"well-posedness":[85],"model,":[89],"derive":[90],"NSFD":[92,119],"scheme,":[93],"investigate":[95],"its":[96],"consistency,":[97],"convergence,":[98],"local":[100],"truncation":[101],"error.":[102],"Numerical":[103],"experiments":[104],"confirm":[105],"theoretical":[107],"results":[108],"demonstrate":[110],"that,":[111],"unlike":[112],"explicit":[115],"FDM,":[116],"avoids":[121],"spurious":[122],"oscillations":[123],"nonphysical":[125],"negative":[126],"solutions":[127],"even":[128],"relatively":[130],"large":[131],"time-step":[132],"sizes.":[133]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}