{"id":"https://openalex.org/W7165638340","doi":"https://doi.org/10.1016/j.camwa.2026.06.018","title":"An adaptive finite difference/ADI scheme with maximum principle preservation for the 2D Allen-Cahn equation with accelerated Caputo derivative evaluation","display_name":"An adaptive finite difference/ADI scheme with maximum principle preservation for the 2D Allen-Cahn equation with accelerated Caputo derivative evaluation","publication_year":2026,"publication_date":"2026-06-23","ids":{"openalex":"https://openalex.org/W7165638340","doi":"https://doi.org/10.1016/j.camwa.2026.06.018"},"language":"en","primary_location":{"id":"doi:10.1016/j.camwa.2026.06.018","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.06.018","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","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/A5057542569","display_name":"Himanshu Kumar Dwivedi","orcid":"https://orcid.org/0000-0002-2829-8764"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Himanshu Kumar Dwivedi","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India"],"raw_orcid":"https://orcid.org/0000-0002-2829-8764","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051619973","display_name":"Rajeev Rajeev","orcid":"https://orcid.org/0000-0002-0787-1517"},"institutions":[{"id":"https://openalex.org/I56404289","display_name":"Indian Institute of Technology BHU","ror":"https://ror.org/01kh5gc44","country_code":"IN","type":"education","lineage":["https://openalex.org/I56404289","https://openalex.org/I91357014"]},{"id":"https://openalex.org/I91357014","display_name":"Banaras Hindu University","ror":"https://ror.org/04cdn2797","country_code":"IN","type":"education","lineage":["https://openalex.org/I91357014"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Rajeev","raw_affiliation_strings":["Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India"],"raw_orcid":"https://orcid.org/0000-0002-0787-1517","affiliations":[{"raw_affiliation_string":"Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221005, India","institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5057542569"],"corresponding_institution_ids":["https://openalex.org/I56404289","https://openalex.org/I91357014"],"apc_list":{"value":3480,"currency":"USD","value_usd":3480},"apc_paid":null,"fwci":7.994,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.9778682,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"217","issue":null,"first_page":"402","last_page":"429"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.28760001063346863,"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"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.28760001063346863,"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"}},{"id":"https://openalex.org/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.21619999408721924,"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.1859000027179718,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.6664999723434448},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.6341999769210815},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.5034999847412109},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.3822000026702881},{"id":"https://openalex.org/keywords/time-derivative","display_name":"Time derivative","score":0.38109999895095825},{"id":"https://openalex.org/keywords/central-differencing-scheme","display_name":"Central differencing scheme","score":0.34470000863075256}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8215000033378601},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.6664999723434448},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.6341999769210815},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5849999785423279},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.5034999847412109},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.42239999771118164},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.3822000026702881},{"id":"https://openalex.org/C17685861","wikidata":"https://www.wikidata.org/wiki/Q6960532","display_name":"Time derivative","level":2,"score":0.38109999895095825},{"id":"https://openalex.org/C157866214","wikidata":"https://www.wikidata.org/wiki/Q17006341","display_name":"Central differencing scheme","level":5,"score":0.34470000863075256},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.321399986743927},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C31010330","wikidata":"https://www.wikidata.org/wiki/Q1914255","display_name":"Maximum principle","level":3,"score":0.26969999074935913},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.25690001249313354},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2549000084400177},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.25440001487731934},{"id":"https://openalex.org/C2776003309","wikidata":"https://www.wikidata.org/wiki/Q1988072","display_name":"Adaptive algorithm","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1016/j.camwa.2026.06.018","is_oa":false,"landing_page_url":"https://doi.org/10.1016/j.camwa.2026.06.018","pdf_url":null,"source":{"id":"https://openalex.org/S4210205691","display_name":"Computers & Mathematics with Applications","issn_l":"0898-1221","issn":["0898-1221","1873-7668"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computers &amp; Mathematics with Applications","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W1512153219","https://openalex.org/W1969312973","https://openalex.org/W1978354679","https://openalex.org/W2004277410","https://openalex.org/W2006333727","https://openalex.org/W2014949681","https://openalex.org/W2036419803","https://openalex.org/W2041001120","https://openalex.org/W2041540906","https://openalex.org/W2046528357","https://openalex.org/W2050969603","https://openalex.org/W2062245988","https://openalex.org/W2062266804","https://openalex.org/W2065232540","https://openalex.org/W2070505112","https://openalex.org/W2119682008","https://openalex.org/W2150388881","https://openalex.org/W2152024595","https://openalex.org/W2593562401","https://openalex.org/W2608656286","https://openalex.org/W2731531705","https://openalex.org/W2741724023","https://openalex.org/W2794616828","https://openalex.org/W2795025401","https://openalex.org/W2799821673","https://openalex.org/W2886181830","https://openalex.org/W2898636786","https://openalex.org/W2898829002","https://openalex.org/W2963309992","https://openalex.org/W2963333235","https://openalex.org/W2963589027","https://openalex.org/W2963781498","https://openalex.org/W2990575151","https://openalex.org/W3014028079","https://openalex.org/W3018009055","https://openalex.org/W3094937669","https://openalex.org/W3095865464","https://openalex.org/W3164684077","https://openalex.org/W4242756898","https://openalex.org/W4401437434","https://openalex.org/W4404165605","https://openalex.org/W7133486477"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":1}],"updated_date":"2026-06-25T06:16:34.145877","created_date":"2026-06-24T00:00:00"}
