{"id":"https://openalex.org/W3118793277","doi":"https://doi.org/10.1080/00207160.2021.1874943","title":"An effective approach for solving a class of nonlinear singular boundary value problems arising in different physical phenomena","display_name":"An effective approach for solving a class of nonlinear singular boundary value problems arising in different physical phenomena","publication_year":2021,"publication_date":"2021-01-14","ids":{"openalex":"https://openalex.org/W3118793277","doi":"https://doi.org/10.1080/00207160.2021.1874943","mag":"3118793277"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2021.1874943","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1874943","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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/A5025516219","display_name":"Saurabh Tomar","orcid":"https://orcid.org/0000-0003-4520-4667"},"institutions":[{"id":"https://openalex.org/I145894827","display_name":"Indian Institute of Technology Kharagpur","ror":"https://ror.org/03w5sq511","country_code":"IN","type":"education","lineage":["https://openalex.org/I145894827"]}],"countries":["IN"],"is_corresponding":true,"raw_author_name":"Saurabh Tomar","raw_affiliation_strings":["Department of Mathematics, Indian Institute of Technology, Kharagpur, India"],"raw_orcid":"https://orcid.org/0000-0003-4520-4667","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Indian Institute of Technology, Kharagpur, India","institution_ids":["https://openalex.org/I145894827"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5025516219"],"corresponding_institution_ids":["https://openalex.org/I145894827"],"apc_list":null,"apc_paid":null,"fwci":1.0155,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.7321993,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":97},"biblio":{"volume":"98","issue":"10","first_page":"2060","last_page":"2077"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.996399998664856,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9958999752998352,"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":0.7701247334480286},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.6127132177352905},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.6025104522705078},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.5620410442352295},{"id":"https://openalex.org/keywords/operator","display_name":"Operator (biology)","score":0.46692511439323425},{"id":"https://openalex.org/keywords/linearization","display_name":"Linearization","score":0.4535249173641205},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4363473653793335},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43032246828079224},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.417934387922287},{"id":"https://openalex.org/keywords/singular-perturbation","display_name":"Singular perturbation","score":0.4109017252922058},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.27953284978866577}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7701247334480286},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.6127132177352905},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.6025104522705078},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.5620410442352295},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.46692511439323425},{"id":"https://openalex.org/C11210021","wikidata":"https://www.wikidata.org/wiki/Q1520713","display_name":"Linearization","level":3,"score":0.4535249173641205},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4363473653793335},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43032246828079224},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.417934387922287},{"id":"https://openalex.org/C165160513","wikidata":"https://www.wikidata.org/wiki/Q7524249","display_name":"Singular perturbation","level":2,"score":0.4109017252922058},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.27953284978866577},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","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/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2021.1874943","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2021.1874943","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","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.4000000059604645}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":47,"referenced_works":["https://openalex.org/W1931696782","https://openalex.org/W1974529299","https://openalex.org/W1976554200","https://openalex.org/W1982426609","https://openalex.org/W1982487488","https://openalex.org/W1983073767","https://openalex.org/W1993650018","https://openalex.org/W1996474089","https://openalex.org/W1996986887","https://openalex.org/W2003033542","https://openalex.org/W2005806366","https://openalex.org/W2006030213","https://openalex.org/W2013446180","https://openalex.org/W2027254911","https://openalex.org/W2028529131","https://openalex.org/W2034835353","https://openalex.org/W2039397492","https://openalex.org/W2042459979","https://openalex.org/W2047605837","https://openalex.org/W2048923395","https://openalex.org/W2053563055","https://openalex.org/W2059024288","https://openalex.org/W2068616545","https://openalex.org/W2069579296","https://openalex.org/W2075201176","https://openalex.org/W2085931380","https://openalex.org/W2094905780","https://openalex.org/W2107221565","https://openalex.org/W2153537517","https://openalex.org/W2194546888","https://openalex.org/W2276969541","https://openalex.org/W2526575642","https://openalex.org/W2530289743","https://openalex.org/W2571132309","https://openalex.org/W2650074445","https://openalex.org/W2745858712","https://openalex.org/W2763937698","https://openalex.org/W2774523565","https://openalex.org/W2805153742","https://openalex.org/W2895479425","https://openalex.org/W2908445374","https://openalex.org/W2914669497","https://openalex.org/W2920382231","https://openalex.org/W2943864324","https://openalex.org/W2962954371","https://openalex.org/W3043766236","https://openalex.org/W3113302407"],"related_works":["https://openalex.org/W2006251942","https://openalex.org/W2364741597","https://openalex.org/W1492103595","https://openalex.org/W1864774435","https://openalex.org/W946352265","https://openalex.org/W3020787026","https://openalex.org/W2334479858","https://openalex.org/W2799209613","https://openalex.org/W2001488143","https://openalex.org/W2392492385"],"abstract_inverted_index":{"In":[0],"this":[1,70],"article,":[2],"an":[3,11,41],"effective":[4],"computational":[5],"technique":[6],"is":[7,54,72],"developed":[8],"to":[9,14,56,61,107],"get":[10],"analytical":[12],"approximation":[13],"the":[15,50,57,63,77,91,99,109,112,116,127,132,136],"solution":[16],"of":[17,20,36,69,79,90,126],"a":[18],"class":[19],"two-point":[21],"nonlinear":[22],"singular":[23],"boundary":[24],"value":[25],"problems":[26,137],"arising":[27],"in":[28],"different":[29],"physical":[30],"models.":[31],"The":[32,67,87],"proposed":[33,92,100,133],"approach":[34,71],"consists":[35],"two":[37],"steps.":[38],"Firstly,":[39],"formulate":[40],"integral":[42,59],"operator":[43,60],"by":[44],"involving":[45],"Green's":[46],"function,":[47],"and":[48,119,122,142],"then,":[49],"Halpern's":[51],"fixed-point":[52],"method":[53,93,101,134],"implemented":[55],"obtained":[58],"establish":[62],"desired":[64],"iterative":[65],"technique.":[66],"convergence":[68],"also":[73],"discussed.":[74],"To":[75],"show":[76],"efficiency":[78],"our":[80],"approach,":[81],"various":[82],"numerical":[83],"examples":[84],"are":[85,97],"considered.":[86],"main":[88],"advantages":[89],"over":[94],"existing":[95],"methods":[96],"that":[98],"does":[102],"not":[103],"require":[104],"Adomian":[105],"polynomials":[106],"handle":[108],"nonlinearity,":[110],"solves":[111],"problem":[113],"without":[114,138],"using":[115],"Lagrange":[117],"multipliers":[118],"constrained":[120],"variations":[121],"takes":[123],"both":[124],"endpoints":[125],"interval":[128],"into":[129],"consideration.":[130],"Further,":[131],"tackles":[135],"requiring":[139],"linearization,":[140],"discretization,":[141],"perturbation":[143],"assumptions,":[144],"unlike":[145],"other":[146],"semi-analytical":[147],"methods.":[148]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":4},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}