{"id":"https://openalex.org/W4391225133","doi":"https://doi.org/10.1080/00207160.2024.2306168","title":"A space-time second-order method based on modified two-grid algorithm with second-order backward difference formula for the extended Fisher\u2013Kolmogorov equation","display_name":"A space-time second-order method based on modified two-grid algorithm with second-order backward difference formula for the extended Fisher\u2013Kolmogorov equation","publication_year":2024,"publication_date":"2024-01-02","ids":{"openalex":"https://openalex.org/W4391225133","doi":"https://doi.org/10.1080/00207160.2024.2306168"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2024.2306168","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2306168","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5100723843","display_name":"Kai Li","orcid":"https://orcid.org/0000-0002-1290-1450"},"institutions":[{"id":"https://openalex.org/I182707071","display_name":"Ludong University","ror":"https://ror.org/028h95t32","country_code":"CN","type":"education","lineage":["https://openalex.org/I182707071"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Kai Li","raw_affiliation_strings":["School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China","institution_ids":["https://openalex.org/I182707071"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073717923","display_name":"Wei Liu","orcid":"https://orcid.org/0000-0002-1970-4951"},"institutions":[{"id":"https://openalex.org/I182707071","display_name":"Ludong University","ror":"https://ror.org/028h95t32","country_code":"CN","type":"education","lineage":["https://openalex.org/I182707071"]},{"id":"https://openalex.org/I4610292","display_name":"Xiangtan University","ror":"https://ror.org/00xsfaz62","country_code":"CN","type":"education","lineage":["https://openalex.org/I4610292"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Wei Liu","raw_affiliation_strings":["School of Mathematics and Computational Science, Xiangtan University, Xiangtan, People's Republic of China","School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Computational Science, Xiangtan University, Xiangtan, People's Republic of China","institution_ids":["https://openalex.org/I4610292"]},{"raw_affiliation_string":"School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China","institution_ids":["https://openalex.org/I182707071"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088745072","display_name":"Yingxue Song","orcid":null},"institutions":[{"id":"https://openalex.org/I182707071","display_name":"Ludong University","ror":"https://ror.org/028h95t32","country_code":"CN","type":"education","lineage":["https://openalex.org/I182707071"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yingxue Song","raw_affiliation_strings":["School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China","institution_ids":["https://openalex.org/I182707071"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5019851705","display_name":"Gexian Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I182707071","display_name":"Ludong University","ror":"https://ror.org/028h95t32","country_code":"CN","type":"education","lineage":["https://openalex.org/I182707071"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gexian Fan","raw_affiliation_strings":["School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics Science, Ludong University, Yantai, People's Republic of China","institution_ids":["https://openalex.org/I182707071"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5073717923"],"corresponding_institution_ids":["https://openalex.org/I182707071","https://openalex.org/I4610292"],"apc_list":null,"apc_paid":null,"fwci":0.3277,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.47828046,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":95},"biblio":{"volume":"101","issue":"1","first_page":"95","last_page":"118"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998000264167786,"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":0.9998000264167786,"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":0.9990000128746033,"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/T11416","display_name":"Numerical methods for differential equations","score":0.9961000084877014,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8009504675865173},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.6337310671806335},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5791997909545898},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.542367160320282},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4542929530143738},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.419086217880249},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.34472304582595825},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.14027884602546692},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.12724703550338745}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8009504675865173},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.6337310671806335},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5791997909545898},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.542367160320282},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4542929530143738},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.419086217880249},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.34472304582595825},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.14027884602546692},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.12724703550338745},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2024.2306168","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2024.2306168","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1740391028","display_name":null,"funder_award_id":"ZR2023MA052","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G3421940315","display_name":null,"funder_award_id":"2021T140576","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"},{"id":"https://openalex.org/G4805622400","display_name":null,"funder_award_id":"2020M672505","funder_id":"https://openalex.org/F4320321543","funder_display_name":"China Postdoctoral Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320321543","display_name":"China Postdoctoral Science Foundation","ror":"https://ror.org/0426zh255"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W1568948019","https://openalex.org/W1980455776","https://openalex.org/W1983119685","https://openalex.org/W2014773752","https://openalex.org/W2014863630","https://openalex.org/W2017786109","https://openalex.org/W2025500042","https://openalex.org/W2033044782","https://openalex.org/W2033653234","https://openalex.org/W2034220943","https://openalex.org/W2034426212","https://openalex.org/W2044228904","https://openalex.org/W2066445588","https://openalex.org/W2075872548","https://openalex.org/W2090305590","https://openalex.org/W2104765972","https://openalex.org/W2115978272","https://openalex.org/W2142856331","https://openalex.org/W2155152088","https://openalex.org/W2166757998","https://openalex.org/W2168771200","https://openalex.org/W2264407536","https://openalex.org/W2346219897","https://openalex.org/W2573255180","https://openalex.org/W2736921035","https://openalex.org/W2740774681","https://openalex.org/W2782523378","https://openalex.org/W2902643746","https://openalex.org/W2921250963","https://openalex.org/W2939120725","https://openalex.org/W3119357403","https://openalex.org/W3151605865","https://openalex.org/W3195518405","https://openalex.org/W3197994490","https://openalex.org/W4285222179","https://openalex.org/W4288057858","https://openalex.org/W4376277706","https://openalex.org/W7028631414"],"related_works":["https://openalex.org/W2017388560","https://openalex.org/W3214346900","https://openalex.org/W60765711","https://openalex.org/W2374124984","https://openalex.org/W1554005152","https://openalex.org/W2356099978","https://openalex.org/W1991990882","https://openalex.org/W2038905316","https://openalex.org/W951292986","https://openalex.org/W2353505767"],"abstract_inverted_index":{"In":[0],"this":[1,136],"paper,":[2],"a":[3,55,60,64,75,88,92],"modified":[4,38,107],"two-grid":[5,39,108],"algorithm":[6,109],"based":[7,41],"on":[8,42,59,87],"block-centred":[9],"finite":[10],"difference":[11,33],"method":[12,40,53],"is":[13,35,45],"developed":[14],"for":[15],"the":[16,25,49,70,80,84,98,106,128,132,142,147],"fourth-order":[17],"nonlinear":[18,50,57],"extended":[19],"Fisher\u2013Kolmogorov":[20],"equation.":[21],"To":[22],"further":[23],"improve":[24],"computational":[26],"efficiency,":[27],"an":[28],"effective":[29],"second-order":[30,112],"accurate":[31],"backward":[32],"formula":[34],"considered.":[36],"The":[37,52,138],"Newton":[43],"iteration":[44],"constructed":[46,78],"to":[47,68,96,126],"linearize":[48],"system.":[51],"solves":[54],"miniature":[56],"system":[58,77],"coarse":[61],"grid":[62,90],"accompanying":[63,91],"larger":[65],"time":[66,94,117],"step":[67,95],"get":[69,97],"numerical":[71,100,122],"solution,":[72],"then":[73],"computes":[74],"linear":[76],"by":[79],"previous":[81],"result":[82,130],"with":[83],"Taylor":[85],"expansion":[86],"fine":[89],"smaller":[93],"correct":[99],"solution.":[101],"Theoretical":[102],"analysis":[103],"shows":[104],"that":[105],"can":[110],"achieve":[111],"convergence":[113],"accuracy":[114],"both":[115],"in":[116],"and":[118,131],"space":[119],"domain.":[120],"Several":[121],"experiments":[123],"are":[124],"provided":[125],"verify":[127],"theoretical":[129],"high":[133],"efficiency":[134],"of":[135,146],"approach.":[137],"practical":[139],"problem":[140],"illustrates":[141],"actual":[143],"applicable":[144],"value":[145],"algorithm.":[148]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-06-15T08:34:33.830935","created_date":"2025-10-10T00:00:00"}
