{"id":"https://openalex.org/W3206478649","doi":"https://doi.org/10.1007/s10915-021-01661-2","title":"Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time\u2013Space Dependent Coefficients","display_name":"Second-Order and Nonuniform Time-Stepping Schemes for Time Fractional Evolution Equations with Time\u2013Space Dependent Coefficients","publication_year":2021,"publication_date":"2021-10-14","ids":{"openalex":"https://openalex.org/W3206478649","doi":"https://doi.org/10.1007/s10915-021-01661-2","mag":"3206478649"},"language":"en","primary_location":{"id":"doi:10.1007/s10915-021-01661-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01661-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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 Scientific 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/A5073521115","display_name":"Pin Lyu","orcid":"https://orcid.org/0000-0002-6947-6838"},"institutions":[{"id":"https://openalex.org/I204831749","display_name":"Southwestern University of Finance and Economics","ror":"https://ror.org/04ewct822","country_code":"CN","type":"education","lineage":["https://openalex.org/I204831749"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Pin Lyu","raw_affiliation_strings":["School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Economic Mathematics, Southwestern University of Finance and Economics, Chengdu, China","institution_ids":["https://openalex.org/I204831749"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5020932623","display_name":"Seakweng Vong","orcid":"https://orcid.org/0000-0002-3017-3346"},"institutions":[{"id":"https://openalex.org/I204512498","display_name":"University of Macau","ror":"https://ror.org/01r4q9n85","country_code":"MO","type":"education","lineage":["https://openalex.org/I204512498"]}],"countries":["MO"],"is_corresponding":true,"raw_author_name":"Seakweng Vong","raw_affiliation_strings":["Department of Mathematics, University of Macau, Macao, China"],"raw_orcid":"https://orcid.org/0000-0002-3017-3346","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Macau, Macao, China","institution_ids":["https://openalex.org/I204512498"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5020932623"],"corresponding_institution_ids":["https://openalex.org/I204512498"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.591,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.63836532,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"89","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":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/T12727","display_name":"Differential Equations and Numerical Methods","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/T11416","display_name":"Numerical methods for differential equations","score":0.9972000122070312,"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":0.8410346508026123},{"id":"https://openalex.org/keywords/space-time","display_name":"Space time","score":0.5957603454589844},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.5723682641983032},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.5001728534698486},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4893905520439148},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46606308221817017},{"id":"https://openalex.org/keywords/spacetime","display_name":"Spacetime","score":0.46554362773895264},{"id":"https://openalex.org/keywords/diffusion","display_name":"Diffusion","score":0.459416925907135},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.44088298082351685},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4331291913986206},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.42898571491241455},{"id":"https://openalex.org/keywords/law","display_name":"Law","score":0.07210254669189453}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8410346508026123},{"id":"https://openalex.org/C96402334","wikidata":"https://www.wikidata.org/wiki/Q3030793","display_name":"Space time","level":2,"score":0.5957603454589844},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5723682641983032},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.5001728534698486},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4893905520439148},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46606308221817017},{"id":"https://openalex.org/C130187892","wikidata":"https://www.wikidata.org/wiki/Q133327","display_name":"Spacetime","level":2,"score":0.46554362773895264},{"id":"https://openalex.org/C69357855","wikidata":"https://www.wikidata.org/wiki/Q163214","display_name":"Diffusion","level":2,"score":0.459416925907135},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.44088298082351685},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4331291913986206},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.42898571491241455},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.07210254669189453},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C42360764","wikidata":"https://www.wikidata.org/wiki/Q83588","display_name":"Chemical engineering","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/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","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},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s10915-021-01661-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s10915-021-01661-2","pdf_url":null,"source":{"id":"https://openalex.org/S151550017","display_name":"Journal of Scientific Computing","issn_l":"0885-7474","issn":["0885-7474","1573-7691"],"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 Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1480520998","display_name":null,"funder_award_id":"0005/2019/A","funder_id":"https://openalex.org/F4320323893","funder_display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia"},{"id":"https://openalex.org/G2369873709","display_name":null,"funder_award_id":"JBK2001002","funder_id":"https://openalex.org/F4320335787","funder_display_name":"Fundamental Research Funds for the Central Universities"},{"id":"https://openalex.org/G3316443298","display_name":null,"funder_award_id":"MYRG2018-00047-FST","funder_id":"https://openalex.org/F4320322841","funder_display_name":"Universidade de Macau"},{"id":"https://openalex.org/G6825331541","display_name":"Rough\u968f\u673a\u6ce2\u52a8\u7387\u6a21\u578b\u7684\u91d1\u878d\u5e94\u7528\u53ca\u7b97\u6cd5\u7814\u7a76","funder_award_id":"12071373","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"},{"id":"https://openalex.org/F4320322841","display_name":"Universidade de Macau","ror":"https://ror.org/01r4q9n85"},{"id":"https://openalex.org/F4320323893","display_name":"Fundo para o Desenvolvimento das Ci\u00eancias e da Tecnologia","ror":"https://ror.org/05vna4324"},{"id":"https://openalex.org/F4320335787","display_name":"Fundamental Research Funds for the Central Universities","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":35,"referenced_works":["https://openalex.org/W15693876","https://openalex.org/W1963952659","https://openalex.org/W1995066738","https://openalex.org/W2025125818","https://openalex.org/W2038375813","https://openalex.org/W2065232540","https://openalex.org/W2068019963","https://openalex.org/W2070451353","https://openalex.org/W2077752008","https://openalex.org/W2111271983","https://openalex.org/W2172005931","https://openalex.org/W2295230376","https://openalex.org/W2535408367","https://openalex.org/W2608656286","https://openalex.org/W2761333852","https://openalex.org/W2787959293","https://openalex.org/W2794616828","https://openalex.org/W2795025401","https://openalex.org/W2799821673","https://openalex.org/W2891433006","https://openalex.org/W2898636786","https://openalex.org/W2963309992","https://openalex.org/W2963392111","https://openalex.org/W2991576200","https://openalex.org/W3013945602","https://openalex.org/W3018009055","https://openalex.org/W3033817112","https://openalex.org/W3037899642","https://openalex.org/W3038217604","https://openalex.org/W3038351969","https://openalex.org/W3098333777","https://openalex.org/W3099925677","https://openalex.org/W3109832867","https://openalex.org/W3164684077","https://openalex.org/W4241253766"],"related_works":["https://openalex.org/W4245687327","https://openalex.org/W2905483137","https://openalex.org/W2072289333","https://openalex.org/W2112549839","https://openalex.org/W4254637135","https://openalex.org/W4365152763","https://openalex.org/W3098062710","https://openalex.org/W4302187300","https://openalex.org/W4293388586","https://openalex.org/W2664576705"],"abstract_inverted_index":null,"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}