{"id":"https://openalex.org/W4280536408","doi":"https://doi.org/10.1080/00207160.2022.2079081","title":"Numerical simulation of high-dimensional two-component reaction\u2013diffusion systems with fractional derivatives","display_name":"Numerical simulation of high-dimensional two-component reaction\u2013diffusion systems with fractional derivatives","publication_year":2022,"publication_date":"2022-05-18","ids":{"openalex":"https://openalex.org/W4280536408","doi":"https://doi.org/10.1080/00207160.2022.2079081"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2022.2079081","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2079081","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/A5038290311","display_name":"Harish Bhatt","orcid":"https://orcid.org/0000-0002-9830-4189"},"institutions":[{"id":"https://openalex.org/I197572798","display_name":"Utah Valley University","ror":"https://ror.org/02rxpxc98","country_code":"US","type":"education","lineage":["https://openalex.org/I197572798"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"H. P. Bhatt","raw_affiliation_strings":["Department of Mathematics, Utah Valley University, Orem, UT, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Utah Valley University, Orem, UT, USA","institution_ids":["https://openalex.org/I197572798"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5038290311"],"corresponding_institution_ids":["https://openalex.org/I197572798"],"apc_list":null,"apc_paid":null,"fwci":0.4058,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.52715569,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"100","issue":"1","first_page":"47","last_page":"68"},"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/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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":0.9990000128746033,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6963436007499695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6335705518722534},{"id":"https://openalex.org/keywords/fractional-calculus","display_name":"Fractional calculus","score":0.5505731701850891},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5335165858268738},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5284155607223511},{"id":"https://openalex.org/keywords/component","display_name":"Component (thermodynamics)","score":0.500802755355835},{"id":"https://openalex.org/keywords/matrix-exponential","display_name":"Matrix exponential","score":0.4973280727863312},{"id":"https://openalex.org/keywords/integrator","display_name":"Integrator","score":0.4963896870613098},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4567905068397522},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.4353683590888977},{"id":"https://openalex.org/keywords/reaction\u2013diffusion-system","display_name":"Reaction\u2013diffusion system","score":0.4278131425380707},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.41299086809158325},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3651135265827179},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2997581958770752},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2406107783317566}],"concepts":[{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6963436007499695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6335705518722534},{"id":"https://openalex.org/C154249771","wikidata":"https://www.wikidata.org/wiki/Q1339058","display_name":"Fractional calculus","level":2,"score":0.5505731701850891},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5335165858268738},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5284155607223511},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.500802755355835},{"id":"https://openalex.org/C195906000","wikidata":"https://www.wikidata.org/wiki/Q1191722","display_name":"Matrix exponential","level":3,"score":0.4973280727863312},{"id":"https://openalex.org/C79518650","wikidata":"https://www.wikidata.org/wiki/Q2081431","display_name":"Integrator","level":3,"score":0.4963896870613098},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4567905068397522},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4353683590888977},{"id":"https://openalex.org/C121231716","wikidata":"https://www.wikidata.org/wiki/Q901210","display_name":"Reaction\u2013diffusion system","level":2,"score":0.4278131425380707},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.41299086809158325},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3651135265827179},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2997581958770752},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2406107783317566},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C2776257435","wikidata":"https://www.wikidata.org/wiki/Q1576430","display_name":"Bandwidth (computing)","level":2,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","level":1,"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/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2022.2079081","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2022.2079081","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1917504514","https://openalex.org/W1963635807","https://openalex.org/W1970532716","https://openalex.org/W1981283442","https://openalex.org/W1984347942","https://openalex.org/W1988715836","https://openalex.org/W1995277785","https://openalex.org/W1997900446","https://openalex.org/W2001744739","https://openalex.org/W2003202721","https://openalex.org/W2009063484","https://openalex.org/W2013668911","https://openalex.org/W2027319740","https://openalex.org/W2043988785","https://openalex.org/W2044815321","https://openalex.org/W2049165066","https://openalex.org/W2062502986","https://openalex.org/W2072825472","https://openalex.org/W2086574007","https://openalex.org/W2088535056","https://openalex.org/W2092797374","https://openalex.org/W2094884329","https://openalex.org/W2111271983","https://openalex.org/W2111828255","https://openalex.org/W2115176036","https://openalex.org/W2134572726","https://openalex.org/W2278928686","https://openalex.org/W2337208398","https://openalex.org/W2786705289","https://openalex.org/W2898993685","https://openalex.org/W2935707000","https://openalex.org/W2962992027","https://openalex.org/W2963745149","https://openalex.org/W2968014749","https://openalex.org/W2977608296","https://openalex.org/W2996958127","https://openalex.org/W3081345820","https://openalex.org/W3106099469","https://openalex.org/W3106303935","https://openalex.org/W3121574170"],"related_works":["https://openalex.org/W2366352762","https://openalex.org/W2613964090","https://openalex.org/W2380425739","https://openalex.org/W2081322886","https://openalex.org/W2349324463","https://openalex.org/W1988313539","https://openalex.org/W1492103595","https://openalex.org/W2364741597","https://openalex.org/W2089476443","https://openalex.org/W2025734700"],"abstract_inverted_index":{"Two-component":[0],"reaction\u2013diffusion":[1,56],"models":[2],"in":[3,41,59,81,87,127],"high":[4,60],"dimensions":[5,132],"involving":[6],"space-fractional":[7,55],"derivatives":[8],"are":[9,124],"used":[10],"as":[11],"a":[12,64,76],"powerful":[13],"modelling":[14],"approach":[15,114],"for":[16],"understanding":[17],"several":[18],"aspects":[19],"of":[20,52,92,140],"spatial":[21],"heterogeneity":[22],"and":[23,34,43,83,115,129,137],"nonlocality.":[24],"In":[25],"this":[26],"paper,":[27],"we":[28,69],"propose":[29],"an":[30,84],"accurate,":[31],"unconditionally":[32],"stable,":[33],"maximum":[35],"principle":[36],"preserving":[37],"fourth-order":[38,66],"method":[39,94],"both":[40],"space":[42,82,131],"time":[44],"variables":[45],"to":[46,133],"study":[47],"the":[48,71,93,100,107,111,118,135,141],"complex":[49],"dynamical":[50],"processes":[51],"two-component":[53],"nonlinear":[54],"systems":[57],"posed":[58],"dimensions.":[61],"To":[62],"achieve":[63],"fast":[65,77],"accurate":[67],"method,":[68],"adapt":[70],"matrix":[72,103,112],"transfer":[73],"technique":[74],"with":[75,110],"Fourier":[78],"transform-based":[79],"implementation":[80],"exponential":[85],"integrator":[86],"time.":[88],"The":[89],"main":[90],"advantage":[91],"is":[95],"that":[96],"it":[97],"avoids":[98],"storing":[99],"large":[101],"dense":[102],"resulting":[104],"from":[105],"discretizing":[106],"fractional":[108],"operator":[109],"transform":[113],"significantly":[116],"reduces":[117],"computational":[119,138],"costs.":[120],"Some":[121],"numerical":[122],"experiments":[123],"carried":[125],"out":[126],"two":[128],"three":[130],"demonstrate":[134],"accuracy":[136],"efficiency":[139],"method.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}