{"id":"https://openalex.org/W4415783814","doi":"https://doi.org/10.1007/s10915-025-03100-y","title":"An Auxiliary Dissipative Functional and Numerical Analysis with $$L_1$$ methods and Convex Splitting Method to Time Fractional Allen-Cahn Equation","display_name":"An Auxiliary Dissipative Functional and Numerical Analysis with $$L_1$$ methods and Convex Splitting Method to Time Fractional Allen-Cahn Equation","publication_year":2025,"publication_date":"2025-11-03","ids":{"openalex":"https://openalex.org/W4415783814","doi":"https://doi.org/10.1007/s10915-025-03100-y"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-025-03100-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03100-y","pdf_url":null,"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":null,"license_id":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5111134569","display_name":"Bing\u2010Ze Lu","orcid":null},"institutions":[{"id":"https://openalex.org/I148099254","display_name":"National Chung Cheng University","ror":"https://ror.org/0028v3876","country_code":"TW","type":"education","lineage":["https://openalex.org/I148099254"]},{"id":"https://openalex.org/I91807558","display_name":"National Cheng Kung University","ror":"https://ror.org/01b8kcc49","country_code":"TW","type":"education","lineage":["https://openalex.org/I91807558"]}],"countries":["TW"],"is_corresponding":true,"raw_author_name":"Bing-Ze Lu","raw_affiliation_strings":["Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Rd, Tainan, 70101, Taiwan","Department of Mathematics, National Chung Cheng University, No.168, Sec. 1, University Rd., Minhsiung, Chiayi, 621301, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Rd, Tainan, 70101, Taiwan","institution_ids":["https://openalex.org/I91807558"]},{"raw_affiliation_string":"Department of Mathematics, National Chung Cheng University, No.168, Sec. 1, University Rd., Minhsiung, Chiayi, 621301, Taiwan","institution_ids":["https://openalex.org/I148099254"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5053357842","display_name":"Yu\u2010Chen Shu","orcid":"https://orcid.org/0000-0002-6450-7076"},"institutions":[{"id":"https://openalex.org/I91807558","display_name":"National Cheng Kung University","ror":"https://ror.org/01b8kcc49","country_code":"TW","type":"education","lineage":["https://openalex.org/I91807558"]}],"countries":["TW"],"is_corresponding":false,"raw_author_name":"Yu-Chen Shu","raw_affiliation_strings":["Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Rd, Tainan, 70101, Taiwan"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, National Cheng Kung University, No. 1, Dasyue Rd, Tainan, 70101, Taiwan","institution_ids":["https://openalex.org/I91807558"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5111134569"],"corresponding_institution_ids":["https://openalex.org/I148099254","https://openalex.org/I91807558"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.31103556,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"105","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.7384999990463257,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.7384999990463257,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11087","display_name":"Solidification and crystal growth phenomena","score":0.12970000505447388,"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"}},{"id":"https://openalex.org/T11205","display_name":"Numerical methods in inverse problems","score":0.016599999740719795,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/dissipative-system","display_name":"Dissipative system","score":0.7829999923706055},{"id":"https://openalex.org/keywords/dissipation","display_name":"Dissipation","score":0.5767999887466431},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.564300000667572},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5393999814987183},{"id":"https://openalex.org/keywords/regular-polygon","display_name":"Regular polygon","score":0.45010000467300415},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4496999979019165},{"id":"https://openalex.org/keywords/convex-analysis","display_name":"Convex analysis","score":0.4447000026702881},{"id":"https://openalex.org/keywords/energy-functional","display_name":"Energy functional","score":0.423799991607666},{"id":"https://openalex.org/keywords/convex-combination","display_name":"Convex combination","score":0.42260000109672546}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8328999876976013},{"id":"https://openalex.org/C99692599","wikidata":"https://www.wikidata.org/wiki/Q596577","display_name":"Dissipative system","level":2,"score":0.7829999923706055},{"id":"https://openalex.org/C135402231","wikidata":"https://www.wikidata.org/wiki/Q898440","display_name":"Dissipation","level":2,"score":0.5767999887466431},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.564300000667572},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5393999814987183},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5113999843597412},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4916999936103821},{"id":"https://openalex.org/C112680207","wikidata":"https://www.wikidata.org/wiki/Q714886","display_name":"Regular polygon","level":2,"score":0.45010000467300415},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4496999979019165},{"id":"https://openalex.org/C12108790","wikidata":"https://www.wikidata.org/wiki/Q2234833","display_name":"Convex analysis","level":4,"score":0.4447000026702881},{"id":"https://openalex.org/C191640071","wikidata":"https://www.wikidata.org/wiki/Q5377056","display_name":"Energy functional","level":2,"score":0.423799991607666},{"id":"https://openalex.org/C111110010","wikidata":"https://www.wikidata.org/wiki/Q2627315","display_name":"Convex combination","level":4,"score":0.42260000109672546},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4056999981403351},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C157972887","wikidata":"https://www.wikidata.org/wiki/Q463359","display_name":"Convex optimization","level":3,"score":0.38350000977516174},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.35109999775886536},{"id":"https://openalex.org/C72134830","wikidata":"https://www.wikidata.org/wiki/Q5166524","display_name":"Convexity","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.32190001010894775},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.3172999918460846},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.3082999885082245},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2996000051498413},{"id":"https://openalex.org/C145446738","wikidata":"https://www.wikidata.org/wiki/Q319913","display_name":"Convex function","level":3,"score":0.2987000048160553},{"id":"https://openalex.org/C186370098","wikidata":"https://www.wikidata.org/wiki/Q442787","display_name":"Energy (signal processing)","level":2,"score":0.29010000824928284},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.2870999872684479},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.2815999984741211},{"id":"https://openalex.org/C148043351","wikidata":"https://www.wikidata.org/wiki/Q4456944","display_name":"Current (fluid)","level":2,"score":0.2791000008583069},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.27639999985694885},{"id":"https://openalex.org/C205147927","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-025-03100-y","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-025-03100-y","pdf_url":null,"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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1726363148","display_name":null,"funder_award_id":"111-2115-M-006-019","funder_id":"https://openalex.org/F2461203286","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G2274592665","display_name":null,"funder_award_id":"113-2917-I-564-033","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"},{"id":"https://openalex.org/G3675635583","display_name":null,"funder_award_id":"112-2119- M-006-004","funder_id":"https://openalex.org/F4320331164","funder_display_name":"National Science and Technology Council"}],"funders":[{"id":"https://openalex.org/F2461203286","display_name":"National Science and Technology Council","ror":"https://ror.org/02kv4zf79"},{"id":"https://openalex.org/F4320331164","display_name":"National Science and Technology Council","ror":"https://ror.org/00wnb9798"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":25,"referenced_works":["https://openalex.org/W2062266804","https://openalex.org/W2073659542","https://openalex.org/W2093685032","https://openalex.org/W2128204029","https://openalex.org/W2601627861","https://openalex.org/W2608656286","https://openalex.org/W2619423951","https://openalex.org/W2894803565","https://openalex.org/W2948855089","https://openalex.org/W2955920149","https://openalex.org/W2964236115","https://openalex.org/W2990575151","https://openalex.org/W3027508994","https://openalex.org/W3037021529","https://openalex.org/W3094937669","https://openalex.org/W3100497057","https://openalex.org/W3105047447","https://openalex.org/W3148434010","https://openalex.org/W3205272164","https://openalex.org/W4226021311","https://openalex.org/W4387060492","https://openalex.org/W4394574286","https://openalex.org/W4400036370","https://openalex.org/W4402458019","https://openalex.org/W4411186254"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-06-13T06:13:01.061226","created_date":"2025-11-03T00:00:00"}
