{"id":"https://openalex.org/W3024780696","doi":"https://doi.org/10.1007/s40314-020-01170-2","title":"A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs","display_name":"A new stable finite difference scheme and its convergence for time-delayed singularly perturbed parabolic PDEs","publication_year":2020,"publication_date":"2020-05-14","ids":{"openalex":"https://openalex.org/W3024780696","doi":"https://doi.org/10.1007/s40314-020-01170-2","mag":"3024780696"},"language":"en","primary_location":{"id":"doi:10.1007/s40314-020-01170-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01170-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied 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/A5011186007","display_name":"P. Pramod Chakravarthy","orcid":"https://orcid.org/0000-0002-5540-6302"},"institutions":[{"id":"https://openalex.org/I167153416","display_name":"Visvesvaraya National Institute of Technology","ror":"https://ror.org/02zrtpp84","country_code":"IN","type":"education","lineage":["https://openalex.org/I167153416"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Pramod Chakravarthy Podila","raw_affiliation_strings":["Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India","institution_ids":["https://openalex.org/I167153416"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026499137","display_name":"Kamalesh Kumar","orcid":"https://orcid.org/0000-0002-2527-3836"},"institutions":[{"id":"https://openalex.org/I167153416","display_name":"Visvesvaraya National Institute of Technology","ror":"https://ror.org/02zrtpp84","country_code":"IN","type":"education","lineage":["https://openalex.org/I167153416"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kamalesh Kumar","raw_affiliation_strings":["Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur, 440010, India","institution_ids":["https://openalex.org/I167153416"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5011186007"],"corresponding_institution_ids":["https://openalex.org/I167153416"],"apc_list":null,"apc_paid":null,"fwci":5.0217,"has_fulltext":false,"cited_by_count":25,"citation_normalized_percentile":{"value":0.96272134,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"39","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":1.0,"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/T12100","display_name":"Advanced Mathematical Modeling in Engineering","score":0.9490000009536743,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.704868495464325},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.6756432056427002},{"id":"https://openalex.org/keywords/finite-difference-scheme","display_name":"Finite difference scheme","score":0.6347717046737671},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5998082160949707},{"id":"https://openalex.org/keywords/scheme","display_name":"Scheme (mathematics)","score":0.5881674289703369},{"id":"https://openalex.org/keywords/perturbation","display_name":"Perturbation (astronomy)","score":0.5555199980735779},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.525223970413208},{"id":"https://openalex.org/keywords/finite-difference","display_name":"Finite difference","score":0.5124895572662354},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46807727217674255},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4615153968334198},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4595031440258026},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4324982464313507},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.36989545822143555},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.177592933177948},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08858075737953186}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.704868495464325},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.6756432056427002},{"id":"https://openalex.org/C2988766672","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference scheme","level":2,"score":0.6347717046737671},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5998082160949707},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.5881674289703369},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.5555199980735779},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.525223970413208},{"id":"https://openalex.org/C181330731","wikidata":"https://www.wikidata.org/wiki/Q2068418","display_name":"Finite difference","level":2,"score":0.5124895572662354},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46807727217674255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4615153968334198},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4595031440258026},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4324982464313507},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.36989545822143555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.177592933177948},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08858075737953186},{"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s40314-020-01170-2","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s40314-020-01170-2","pdf_url":null,"source":{"id":"https://openalex.org/S4210195884","display_name":"Computational and Applied Mathematics","issn_l":"1807-0302","issn":["1807-0302","2238-3603"],"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":"Computational and Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.5299999713897705,"display_name":"Climate action","id":"https://metadata.un.org/sdg/13"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":23,"referenced_works":["https://openalex.org/W79873316","https://openalex.org/W577049880","https://openalex.org/W1605753492","https://openalex.org/W2010334941","https://openalex.org/W2014064271","https://openalex.org/W2018032381","https://openalex.org/W2036371403","https://openalex.org/W2059204953","https://openalex.org/W2070043289","https://openalex.org/W2081738893","https://openalex.org/W2091574526","https://openalex.org/W2123117227","https://openalex.org/W2322859696","https://openalex.org/W2331626267","https://openalex.org/W2384137058","https://openalex.org/W2579746777","https://openalex.org/W2585001253","https://openalex.org/W2765430266","https://openalex.org/W2790373273","https://openalex.org/W3203680921","https://openalex.org/W3205493946","https://openalex.org/W4241946322","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W2330640442","https://openalex.org/W2392533133","https://openalex.org/W2085654163","https://openalex.org/W2372700288","https://openalex.org/W1975234065","https://openalex.org/W2983915667","https://openalex.org/W799252160","https://openalex.org/W1520852618","https://openalex.org/W2073035836","https://openalex.org/W2370641521"],"abstract_inverted_index":null,"counts_by_year":[{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":9},{"year":2022,"cited_by_count":4},{"year":2021,"cited_by_count":4}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}