{"id":"https://openalex.org/W7118064987","doi":"https://doi.org/10.1007/s12190-025-02743-2","title":"Modified L2-1$$_{\\sigma}$$ schemes coupled with a spectral method for solving the time-space fractional diffusion equation containing the fractional Laplacian","display_name":"Modified L2-1$$_{\\sigma}$$ schemes coupled with a spectral method for solving the time-space fractional diffusion equation containing the fractional Laplacian","publication_year":2026,"publication_date":"2026-01-03","ids":{"openalex":"https://openalex.org/W7118064987","doi":"https://doi.org/10.1007/s12190-025-02743-2"},"language":"en","primary_location":{"id":"doi:10.1007/s12190-025-02743-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-025-02743-2","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"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 Applied Mathematics and 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/A5112119256","display_name":"Fan Liu","orcid":null},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Fan Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5121846028","display_name":"Mei Yin","orcid":null},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mei Yin","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China","institution_ids":["https://openalex.org/I178232147"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5033242350","display_name":"Hongyan LIU","orcid":null},"institutions":[{"id":"https://openalex.org/I178232147","display_name":"Guizhou University","ror":"https://ror.org/02wmsc916","country_code":"CN","type":"education","lineage":["https://openalex.org/I178232147"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hongyan Liu","raw_affiliation_strings":["School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, 550025, China","institution_ids":["https://openalex.org/I178232147"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5112119256"],"corresponding_institution_ids":["https://openalex.org/I178232147"],"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":0.02277132,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"72","issue":"2","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":0.9765999913215637,"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":0.9765999913215637,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.009100000374019146,"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/T10248","display_name":"Nonlinear Waves and Solitons","score":0.0034000000450760126,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5788000226020813},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.5443000197410583},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5350000262260437},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.5029000043869019},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.4749000072479248},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.44920000433921814},{"id":"https://openalex.org/keywords/fourier-transform","display_name":"Fourier transform","score":0.40220001339912415},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.397599995136261},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.33640000224113464}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7854999899864197},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5788000226020813},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.5443000197410583},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5350000262260437},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5127000212669373},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.5029000043869019},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.4749000072479248},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.44920000433921814},{"id":"https://openalex.org/C102519508","wikidata":"https://www.wikidata.org/wiki/Q6520159","display_name":"Fourier transform","level":2,"score":0.40220001339912415},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.397599995136261},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3449999988079071},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.33640000224113464},{"id":"https://openalex.org/C31487907","wikidata":"https://www.wikidata.org/wiki/Q1154597","display_name":"Polygon mesh","level":2,"score":0.3352000117301941},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.3262999951839447},{"id":"https://openalex.org/C571446","wikidata":"https://www.wikidata.org/wiki/Q6510183","display_name":"Diffusion equation","level":3,"score":0.3122999966144562},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.31040000915527344},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.3100999891757965},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.30799999833106995},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.3034999966621399},{"id":"https://openalex.org/C2775913539","wikidata":"https://www.wikidata.org/wiki/Q30694381","display_name":"Fractional Laplacian","level":2,"score":0.29319998621940613},{"id":"https://openalex.org/C177937620","wikidata":"https://www.wikidata.org/wiki/Q7254447","display_name":"Pseudo-spectral method","level":4,"score":0.28780001401901245},{"id":"https://openalex.org/C520416788","wikidata":"https://www.wikidata.org/wiki/Q5419229","display_name":"Exact solutions in general relativity","level":2,"score":0.2842999994754791},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.2838999927043915},{"id":"https://openalex.org/C57733114","wikidata":"https://www.wikidata.org/wiki/Q1006032","display_name":"Discrete Fourier transform (general)","level":5,"score":0.2800999879837036},{"id":"https://openalex.org/C203024314","wikidata":"https://www.wikidata.org/wiki/Q1365258","display_name":"Fourier analysis","level":3,"score":0.2637999951839447},{"id":"https://openalex.org/C207864730","wikidata":"https://www.wikidata.org/wiki/Q179467","display_name":"Fourier series","level":2,"score":0.2554999887943268}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s12190-025-02743-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s12190-025-02743-2","pdf_url":null,"source":{"id":"https://openalex.org/S199913245","display_name":"Journal of Applied Mathematics and Computing","issn_l":"1598-5865","issn":["1598-5865","1865-2085"],"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 Applied Mathematics and Computing","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":32,"referenced_works":["https://openalex.org/W1984898295","https://openalex.org/W2062266804","https://openalex.org/W2065232540","https://openalex.org/W2075099215","https://openalex.org/W2111271983","https://openalex.org/W2165076033","https://openalex.org/W2294672943","https://openalex.org/W2608656286","https://openalex.org/W2741724023","https://openalex.org/W2769258003","https://openalex.org/W2809985151","https://openalex.org/W2898636786","https://openalex.org/W2943306774","https://openalex.org/W2963309992","https://openalex.org/W2982546823","https://openalex.org/W3008175267","https://openalex.org/W3014028079","https://openalex.org/W3021314105","https://openalex.org/W3099709074","https://openalex.org/W3121070290","https://openalex.org/W3164559554","https://openalex.org/W4285388960","https://openalex.org/W4301223505","https://openalex.org/W4321460201","https://openalex.org/W4386377660","https://openalex.org/W4391991407","https://openalex.org/W4394931292","https://openalex.org/W4395678319","https://openalex.org/W4399693453","https://openalex.org/W4401947755","https://openalex.org/W4408323511","https://openalex.org/W4411493424"],"related_works":[],"abstract_inverted_index":null,"counts_by_year":[],"updated_date":"2026-01-03T23:12:46.507823","created_date":"2026-01-03T00:00:00"}
