{"id":"https://openalex.org/W2626148257","doi":"https://doi.org/10.1080/00207160.2017.1343941","title":"Numerical methods for fractional partial differential equations","display_name":"Numerical methods for fractional partial differential equations","publication_year":2017,"publication_date":"2017-06-16","ids":{"openalex":"https://openalex.org/W2626148257","doi":"https://doi.org/10.1080/00207160.2017.1343941","mag":"2626148257"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2017.1343941","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1343941","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/A5088246745","display_name":"Changpin Li","orcid":"https://orcid.org/0000-0003-2012-2788"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Changpin Li","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100687057","display_name":"An Chen","orcid":"https://orcid.org/0000-0003-2165-5746"},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"An Chen","raw_affiliation_strings":["Department of Mathematics, Shanghai University, Shanghai, China"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Shanghai University, Shanghai, China","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5088246745"],"corresponding_institution_ids":["https://openalex.org/I113940042"],"apc_list":null,"apc_paid":null,"fwci":7.7081,"has_fulltext":false,"cited_by_count":145,"citation_normalized_percentile":{"value":0.97897319,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":"95","issue":"6-7","first_page":"1048","last_page":"1099"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9998999834060669,"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":0.9998999834060669,"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/T10514","display_name":"Numerical methods in engineering","score":0.9965000152587891,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"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/T10822","display_name":"Acoustic Wave Phenomena Research","score":0.9916999936103821,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8068890571594238},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.6538300514221191},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.62518310546875},{"id":"https://openalex.org/keywords/numerical-partial-differential-equations","display_name":"Numerical partial differential equations","score":0.6064708828926086},{"id":"https://openalex.org/keywords/galerkin-method","display_name":"Galerkin method","score":0.5375051498413086},{"id":"https://openalex.org/keywords/spectral-method","display_name":"Spectral method","score":0.49548137187957764},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47119924426078796},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.4654327929019928},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4339388310909271},{"id":"https://openalex.org/keywords/first-order-partial-differential-equation","display_name":"First-order partial differential equation","score":0.4218364953994751},{"id":"https://openalex.org/keywords/space","display_name":"Space (punctuation)","score":0.41131800413131714},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1035262942314148},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.04921659827232361}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8068890571594238},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.6538300514221191},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.62518310546875},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.6064708828926086},{"id":"https://openalex.org/C186899397","wikidata":"https://www.wikidata.org/wiki/Q1491980","display_name":"Galerkin method","level":3,"score":0.5375051498413086},{"id":"https://openalex.org/C23463724","wikidata":"https://www.wikidata.org/wiki/Q2308831","display_name":"Spectral method","level":2,"score":0.49548137187957764},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47119924426078796},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.4654327929019928},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4339388310909271},{"id":"https://openalex.org/C64057670","wikidata":"https://www.wikidata.org/wiki/Q4381442","display_name":"First-order partial differential equation","level":3,"score":0.4218364953994751},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.41131800413131714},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1035262942314148},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.04921659827232361},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2017.1343941","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2017.1343941","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/G6815574861","display_name":null,"funder_award_id":"11372170","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7388677852","display_name":null,"funder_award_id":"11632008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G809826743","display_name":null,"funder_award_id":"11671251","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":213,"referenced_works":["https://openalex.org/W620183161","https://openalex.org/W755756226","https://openalex.org/W827524955","https://openalex.org/W833140947","https://openalex.org/W877810758","https://openalex.org/W902939226","https://openalex.org/W1127902823","https://openalex.org/W1436001274","https://openalex.org/W1510837990","https://openalex.org/W1530054495","https://openalex.org/W1564464599","https://openalex.org/W1571391776","https://openalex.org/W1655132380","https://openalex.org/W1786936588","https://openalex.org/W1945420166","https://openalex.org/W1953136735","https://openalex.org/W1963803459","https://openalex.org/W1964804260","https://openalex.org/W1965266992","https://openalex.org/W1965557233","https://openalex.org/W1966513244","https://openalex.org/W1968501254","https://openalex.org/W1969312973","https://openalex.org/W1969734198","https://openalex.org/W1970546830","https://openalex.org/W1971417052","https://openalex.org/W1974043434","https://openalex.org/W1974267666","https://openalex.org/W1976371327","https://openalex.org/W1977696410","https://openalex.org/W1978354679","https://openalex.org/W1980154613","https://openalex.org/W1983001687","https://openalex.org/W1984091802","https://openalex.org/W1986544454","https://openalex.org/W1986915637","https://openalex.org/W1988087043","https://openalex.org/W1989188636","https://openalex.org/W1990829983","https://openalex.org/W1991982189","https://openalex.org/W1992526128","https://openalex.org/W1995597760","https://openalex.org/W1996761814","https://openalex.org/W1997432471","https://openalex.org/W1998175738","https://openalex.org/W1999695483","https://openalex.org/W2000526322","https://openalex.org/W2000659785","https://openalex.org/W2001011967","https://openalex.org/W2001031344","https://openalex.org/W2003202721","https://openalex.org/W2003437637","https://openalex.org/W2006044588","https://openalex.org/W2006359060","https://openalex.org/W2006850990","https://openalex.org/W2008247388","https://openalex.org/W2009063484","https://openalex.org/W2012163408","https://openalex.org/W2013129097","https://openalex.org/W2013668911","https://openalex.org/W2014666630","https://openalex.org/W2016823491","https://openalex.org/W2020772937","https://openalex.org/W2022694169","https://openalex.org/W2024093795","https://openalex.org/W2026634373","https://openalex.org/W2027692276","https://openalex.org/W2028586620","https://openalex.org/W2029529153","https://openalex.org/W2030146312","https://openalex.org/W2032744100","https://openalex.org/W2033471049","https://openalex.org/W2033593438","https://openalex.org/W2035830378","https://openalex.org/W2037274488","https://openalex.org/W2038588805","https://openalex.org/W2039707205","https://openalex.org/W2040558735","https://openalex.org/W2041202720","https://openalex.org/W2042535847","https://openalex.org/W2043080303","https://openalex.org/W2043617602","https://openalex.org/W2044311469","https://openalex.org/W2045504118","https://openalex.org/W2047594597","https://openalex.org/W2048805000","https://openalex.org/W2049030310","https://openalex.org/W2050580331","https://openalex.org/W2052623210","https://openalex.org/W2053256951","https://openalex.org/W2054899953","https://openalex.org/W2055148154","https://openalex.org/W2055241441","https://openalex.org/W2056061743","https://openalex.org/W2056390784","https://openalex.org/W2056829543","https://openalex.org/W2057119166","https://openalex.org/W2057748165","https://openalex.org/W2059607966","https://openalex.org/W2062092992","https://openalex.org/W2062266804","https://openalex.org/W2062650267","https://openalex.org/W2062714751","https://openalex.org/W2063052480","https://openalex.org/W2064301689","https://openalex.org/W2065232540","https://openalex.org/W2065254635","https://openalex.org/W2065390423","https://openalex.org/W2066693071","https://openalex.org/W2068610405","https://openalex.org/W2071268148","https://openalex.org/W2074077397","https://openalex.org/W2080928512","https://openalex.org/W2081811871","https://openalex.org/W2081871678","https://openalex.org/W2083046996","https://openalex.org/W2084142728","https://openalex.org/W2085534818","https://openalex.org/W2086512227","https://openalex.org/W2088826361","https://openalex.org/W2091244859","https://openalex.org/W2091740033","https://openalex.org/W2092146111","https://openalex.org/W2092718516","https://openalex.org/W2092912961","https://openalex.org/W2093225350","https://openalex.org/W2093685032","https://openalex.org/W2094384405","https://openalex.org/W2094838226","https://openalex.org/W2104736025","https://openalex.org/W2105723279","https://openalex.org/W2107162131","https://openalex.org/W2110504259","https://openalex.org/W2111271983","https://openalex.org/W2114010261","https://openalex.org/W2114137384","https://openalex.org/W2118160506","https://openalex.org/W2118288723","https://openalex.org/W2118816806","https://openalex.org/W2119671522","https://openalex.org/W2123426570","https://openalex.org/W2124303144","https://openalex.org/W2124718863","https://openalex.org/W2125526756","https://openalex.org/W2127684492","https://openalex.org/W2130994331","https://openalex.org/W2138935277","https://openalex.org/W2139559416","https://openalex.org/W2140057174","https://openalex.org/W2141494273","https://openalex.org/W2142758723","https://openalex.org/W2144367930","https://openalex.org/W2161701360","https://openalex.org/W2164841187","https://openalex.org/W2164946476","https://openalex.org/W2165076033","https://openalex.org/W2170885741","https://openalex.org/W2187652788","https://openalex.org/W2192767319","https://openalex.org/W2201436390","https://openalex.org/W2215263022","https://openalex.org/W2220122545","https://openalex.org/W2229552618","https://openalex.org/W2230775999","https://openalex.org/W2234614486","https://openalex.org/W2267852856","https://openalex.org/W2271295549","https://openalex.org/W2274070693","https://openalex.org/W2279965344","https://openalex.org/W2294672943","https://openalex.org/W2304262673","https://openalex.org/W2308477722","https://openalex.org/W2309383193","https://openalex.org/W2318099151","https://openalex.org/W2331583843","https://openalex.org/W2334407529","https://openalex.org/W2340358137","https://openalex.org/W2345986302","https://openalex.org/W2360890442","https://openalex.org/W2479180925","https://openalex.org/W2488513708","https://openalex.org/W2489930379","https://openalex.org/W2510732450","https://openalex.org/W2512423899","https://openalex.org/W2552773392","https://openalex.org/W2567477586","https://openalex.org/W2577996109","https://openalex.org/W2583019075","https://openalex.org/W2586480731","https://openalex.org/W2587540480","https://openalex.org/W2588029474","https://openalex.org/W2591246667","https://openalex.org/W2591810306","https://openalex.org/W2592662912","https://openalex.org/W2593135059","https://openalex.org/W2605247189","https://openalex.org/W2605580434","https://openalex.org/W2610018898","https://openalex.org/W2626486898","https://openalex.org/W2729772172","https://openalex.org/W2765519574","https://openalex.org/W2787959293","https://openalex.org/W2963020731","https://openalex.org/W2963309992","https://openalex.org/W2963541513","https://openalex.org/W2963825988","https://openalex.org/W2963919450","https://openalex.org/W2988078269","https://openalex.org/W3101361006","https://openalex.org/W3102859449","https://openalex.org/W3104584423","https://openalex.org/W3105813679","https://openalex.org/W3106522901"],"related_works":["https://openalex.org/W2020570337","https://openalex.org/W1970590191","https://openalex.org/W2978094276","https://openalex.org/W2056658486","https://openalex.org/W2111171090","https://openalex.org/W2096756136","https://openalex.org/W3022381199","https://openalex.org/W4293168753","https://openalex.org/W2348286450","https://openalex.org/W4256084332"],"abstract_inverted_index":{"In":[0],"this":[1],"review":[2],"paper,":[3],"we":[4],"are":[5,29,47],"mainly":[6],"concerned":[7],"with":[8],"the":[9,13,19,32,45],"finite":[10,15],"difference":[11],"methods,":[12,17],"Galerkin":[14],"element":[16],"and":[18,35],"spectral":[20],"methods":[21],"for":[22,44,56],"fractional":[23],"partial":[24,37],"differential":[25,38],"equations":[26,39],"(FPDEs),":[27],"which":[28],"divided":[30],"into":[31],"time-fractional,":[33],"space-fractional,":[34],"space-time-fractional":[36],"(PDEs).":[40],"Besides,":[41],"fast":[42],"algorithms":[43,55],"FPDEs":[46],"included":[48],"in":[49],"order":[50],"to":[51],"stimulate":[52],"more":[53],"efficient":[54],"high-dimensional":[57],"FPDEs.":[58]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":20},{"year":2024,"cited_by_count":22},{"year":2023,"cited_by_count":19},{"year":2022,"cited_by_count":14},{"year":2021,"cited_by_count":19},{"year":2020,"cited_by_count":15},{"year":2019,"cited_by_count":16},{"year":2018,"cited_by_count":14},{"year":2017,"cited_by_count":3},{"year":2016,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}