{"id":"https://openalex.org/W2555559514","doi":"https://doi.org/10.1007/978-981-10-2663-8_26","title":"Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher\u2019s Equation","display_name":"Legendre Collocation Spectral Method for Solving Space Fractional Nonlinear Fisher\u2019s Equation","publication_year":2016,"publication_date":"2016-01-01","ids":{"openalex":"https://openalex.org/W2555559514","doi":"https://doi.org/10.1007/978-981-10-2663-8_26","mag":"2555559514"},"language":"en","primary_location":{"id":"doi:10.1007/978-981-10-2663-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-981-10-2663-8_26","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"type":"book-chapter","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1007/978-981-10-2663-8_26","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036881468","display_name":"Zeting Liu","orcid":"https://orcid.org/0000-0001-8574-3206"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zeting Liu","raw_affiliation_strings":["School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5071840139","display_name":"Shujuan Lv","orcid":null},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Shujuan Lv","raw_affiliation_strings":["School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100723332","display_name":"Xiaocui Li","orcid":"https://orcid.org/0000-0002-7209-3272"},"institutions":[{"id":"https://openalex.org/I82880672","display_name":"Beihang University","ror":"https://ror.org/00wk2mp56","country_code":"CN","type":"education","lineage":["https://openalex.org/I82880672"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaocui Li","raw_affiliation_strings":["School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China"],"affiliations":[{"raw_affiliation_string":"School of Mathematics and Systems Science and LMIB, Beihang University, Beijing, 100191, China","institution_ids":["https://openalex.org/I82880672"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5036881468"],"corresponding_institution_ids":["https://openalex.org/I82880672"],"apc_list":null,"apc_paid":null,"fwci":0.8523,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.77173913,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"245","last_page":"252"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":1.0,"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":1.0,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9977999925613403,"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9868000149726868,"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/legendre-polynomials","display_name":"Legendre polynomials","score":0.8326873779296875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7778562307357788},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.6907644271850586},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.6042817234992981},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5831171274185181},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5704327821731567},{"id":"https://openalex.org/keywords/legendre-function","display_name":"Legendre function","score":0.5414112210273743},{"id":"https://openalex.org/keywords/collocation-method","display_name":"Collocation method","score":0.5108820796012878},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.49524202942848206},{"id":"https://openalex.org/keywords/legendres-equation","display_name":"Legendre's equation","score":0.47979408502578735},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4737420976161957},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.41453057527542114},{"id":"https://openalex.org/keywords/associated-legendre-polynomials","display_name":"Associated Legendre polynomials","score":0.4141598343849182},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.1289443075656891},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08982706069946289},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.07461309432983398},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07440134882926941}],"concepts":[{"id":"https://openalex.org/C111458787","wikidata":"https://www.wikidata.org/wiki/Q215405","display_name":"Legendre polynomials","level":2,"score":0.8326873779296875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7778562307357788},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.6907644271850586},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.6042817234992981},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5831171274185181},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5704327821731567},{"id":"https://openalex.org/C153262748","wikidata":"https://www.wikidata.org/wiki/Q17098449","display_name":"Legendre function","level":3,"score":0.5414112210273743},{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.5108820796012878},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.49524202942848206},{"id":"https://openalex.org/C86287605","wikidata":"https://www.wikidata.org/wiki/Q4454970","display_name":"Legendre's equation","level":3,"score":0.47979408502578735},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4737420976161957},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.41453057527542114},{"id":"https://openalex.org/C36956377","wikidata":"https://www.wikidata.org/wiki/Q228376","display_name":"Associated Legendre polynomials","level":5,"score":0.4141598343849182},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.1289443075656891},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08982706069946289},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.07461309432983398},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07440134882926941},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.0},{"id":"https://openalex.org/C78540521","wikidata":"https://www.wikidata.org/wiki/Q1498246","display_name":"Gegenbauer polynomials","level":4,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/978-981-10-2663-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-981-10-2663-8_26","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"}],"best_oa_location":{"id":"doi:10.1007/978-981-10-2663-8_26","is_oa":true,"landing_page_url":"https://doi.org/10.1007/978-981-10-2663-8_26","pdf_url":null,"source":{"id":"https://openalex.org/S2764900261","display_name":"Communications in computer and information science","issn_l":"1865-0929","issn":["1865-0929","1865-0937"],"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":"book series"},"license":"cc-by-nc","license_id":"https://openalex.org/licenses/cc-by-nc","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Communications in Computer and Information Science","raw_type":"book-chapter"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":27,"referenced_works":["https://openalex.org/W640428934","https://openalex.org/W1584611818","https://openalex.org/W1965316397","https://openalex.org/W1969202999","https://openalex.org/W1969308726","https://openalex.org/W1969312973","https://openalex.org/W1975383112","https://openalex.org/W1989047470","https://openalex.org/W2002386912","https://openalex.org/W2012524923","https://openalex.org/W2019324632","https://openalex.org/W2029529153","https://openalex.org/W2034221093","https://openalex.org/W2048805000","https://openalex.org/W2070884726","https://openalex.org/W2091740033","https://openalex.org/W2107162131","https://openalex.org/W2110504259","https://openalex.org/W2111271983","https://openalex.org/W2116640232","https://openalex.org/W2137838471","https://openalex.org/W2142758723","https://openalex.org/W2300268011","https://openalex.org/W2338398715","https://openalex.org/W4247953052","https://openalex.org/W4253937035","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2953361964","https://openalex.org/W2021432593","https://openalex.org/W3200178185","https://openalex.org/W3005861762","https://openalex.org/W1988418937","https://openalex.org/W2323274059","https://openalex.org/W2053826141","https://openalex.org/W3130427480","https://openalex.org/W2183150594","https://openalex.org/W2385237360"],"abstract_inverted_index":{"We":[0,53],"consider":[1],"the":[2,8,15,20,28,56,60,78],"initial":[3],"boundary":[4,29],"value":[5],"problem":[6],"of":[7,59],"space":[9,47],"fractional":[10,21,61],"nonlinear":[11],"Fisher\u2019s":[12,92],"equations":[13],"on":[14],"general":[16],"interval":[17],"(a,b)":[18],"and":[19,48,74,77],"derivative":[22],"is":[23,41,86],"described":[24],"in":[25,46,51],"Caputo":[26],"sense,":[27],"conditions":[30],"are":[31,65],"nonhomogeneous.":[32],"A":[33],"fully":[34],"discrete":[35],"Legendre":[36,70,82],"collocation":[37,71,83],"spectral":[38,72,84],"approximation":[39],"scheme":[40],"structured":[42],"basing":[43],"Legendre-Gauss-Lobatto":[44],"points":[45],"backward":[49],"difference":[50],"time.":[52],"also":[54],"use":[55],"operational":[57],"matrix":[58],"derivative.":[62],"Numerical":[63],"experiments":[64],"presented":[66],"with":[67],"comparisons":[68],"between":[69],"method":[73,85,89],"other":[75],"methods,":[76],"results":[79],"show":[80],"that":[81],"an":[87],"alternative":[88],"for":[90],"solving":[91],"equation.":[93]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":1},{"year":2017,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}