{"id":"https://openalex.org/W7166300663","doi":"https://doi.org/10.1142/s0219876226500465","title":"Modified Cubic B-Spline Based Differential Quadrature Method for Solving Generalized Black\u2013Scholes Equation","display_name":"Modified Cubic B-Spline Based Differential Quadrature Method for Solving Generalized Black\u2013Scholes Equation","publication_year":2026,"publication_date":"2026-06-27","ids":{"openalex":"https://openalex.org/W7166300663","doi":"https://doi.org/10.1142/s0219876226500465"},"language":"en","primary_location":{"id":"doi:10.1142/s0219876226500465","doi":"https://doi.org/10.1142/s0219876226500465","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219876226500465","pdf_url":null,"source":{"id":"https://openalex.org/S42084661","display_name":"International Journal of Computational Methods","issn_l":"0219-8762","issn":["0219-8762","1793-6969"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Methods","raw_type":"journal-article"},"volume":null,"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/A5120397900","display_name":"V Nizamudheen","orcid":"https://orcid.org/0009-0007-7993-877X","observed_orcids":["https://orcid.org/0009-0007-7993-877X"]},"institutions":[{"id":"https://openalex.org/I114176345","display_name":"University of Calicut","ror":"https://ror.org/05yeh3g67","country_code":"IN","type":"education","lineage":["https://openalex.org/I114176345"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"V. Nizamudheen","raw_affiliation_strings":["Department of Mathematics, Farook College (Autonomous), Affiliated to Calicut University, Kozhikode 673632, India"],"raw_orcid":"https://orcid.org/0009-0007-7993-877X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Farook College (Autonomous), Affiliated to Calicut University, Kozhikode 673632, India","institution_ids":["https://openalex.org/I114176345"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065706810","display_name":"Noufal Asharaf","orcid":"https://orcid.org/0000-0002-1150-2343","observed_orcids":["https://orcid.org/0000-0002-1150-2343"]},"institutions":[{"id":"https://openalex.org/I20497027","display_name":"Cochin University of Science and Technology","ror":"https://ror.org/00a4kqq17","country_code":"IN","type":"education","lineage":["https://openalex.org/I20497027"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Noufal Asharaf","raw_affiliation_strings":["Department of Mathematics, CUSAT (Cochin University of Science and Technology), Cochin 682022, India"],"raw_orcid":"https://orcid.org/0000-0002-1150-2343","affiliations":[{"raw_affiliation_string":"Department of Mathematics, CUSAT (Cochin University of Science and Technology), Cochin 682022, India","institution_ids":["https://openalex.org/I20497027"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112864880","display_name":"T. K. Riyasudheen","orcid":"https://orcid.org/0000-0002-0792-8659","observed_orcids":["https://orcid.org/0000-0002-0792-8659"]},"institutions":[{"id":"https://openalex.org/I4405285013","display_name":"Indian Institute of Information Technology Kottayam","ror":"https://ror.org/04mj1ps34","country_code":"IN","type":"education","lineage":["https://openalex.org/I4405285013"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"T. K. Riyasudheen","raw_affiliation_strings":["Department of Computational Science and Humanities, Indian Institute of Information Technology Kottayam, Valavoor, Kottayam 686635, Kerala, India"],"raw_orcid":"https://orcid.org/0000-0002-0792-8659","affiliations":[{"raw_affiliation_string":"Department of Computational Science and Humanities, Indian Institute of Information Technology Kottayam, Valavoor, Kottayam 686635, Kerala, India","institution_ids":["https://openalex.org/I4405285013"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114486973","display_name":"T. Shefeeq","orcid":"https://orcid.org/0000-0002-3943-0054","observed_orcids":["https://orcid.org/0000-0002-3943-0054"]},"institutions":[{"id":"https://openalex.org/I114176345","display_name":"University of Calicut","ror":"https://ror.org/05yeh3g67","country_code":"IN","type":"education","lineage":["https://openalex.org/I114176345"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"T. Shefeeq","raw_affiliation_strings":["Department of Mathematics, Farook College (Autonomous), Affiliated to Calicut University, Kozhikode 673632, India"],"raw_orcid":"https://orcid.org/0000-0002-3943-0054","affiliations":[{"raw_affiliation_string":"Department of Mathematics, Farook College (Autonomous), Affiliated to Calicut University, Kozhikode 673632, India","institution_ids":["https://openalex.org/I114176345"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.53986653,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"23","issue":"10","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.24060000479221344,"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/T11416","display_name":"Numerical methods for differential equations","score":0.24060000479221344,"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":0.21940000355243683,"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/T10067","display_name":"Stochastic processes and financial applications","score":0.1898999959230423,"subfield":{"id":"https://openalex.org/subfields/2003","display_name":"Finance"},"field":{"id":"https://openalex.org/fields/20","display_name":"Economics, Econometrics and Finance"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/differential-quadrature-method","display_name":"differential quadrature method","score":0.9980000257492065},{"id":"https://openalex.org/keywords/option-pricing","display_name":"option pricing","score":0.7850000262260437},{"id":"https://openalex.org/keywords/logarithmic-transformation","display_name":"logarithmic transformation","score":0.9440000057220459},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"numerical stability","score":0.621999979019165}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7660999894142151},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6208000183105469},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5515000224113464},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5325999855995178},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.5271999835968018},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.5177000164985657},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.4814999997615814},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.45669999718666077},{"id":"https://openalex.org/C39927690","wikidata":"https://www.wikidata.org/wiki/Q11197","display_name":"Logarithm","level":2,"score":0.4302000105381012},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4242999851703644},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4032000005245209},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.3952000141143799},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.3901999890804291},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.38909998536109924},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.37929999828338623},{"id":"https://openalex.org/C172657837","wikidata":"https://www.wikidata.org/wiki/Q5131618","display_name":"Clenshaw\u2013Curtis quadrature","level":5,"score":0.3366999924182892},{"id":"https://openalex.org/C204241405","wikidata":"https://www.wikidata.org/wiki/Q461499","display_name":"Transformation (genetics)","level":3,"score":0.30979999899864197},{"id":"https://openalex.org/C54691486","wikidata":"https://www.wikidata.org/wiki/Q5527851","display_name":"Gauss\u2013Jacobi quadrature","level":5,"score":0.30489999055862427},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.29820001125335693},{"id":"https://openalex.org/C136798861","wikidata":"https://www.wikidata.org/wiki/Q1826712","display_name":"Method of lines","level":5,"score":0.29649999737739563},{"id":"https://openalex.org/C78727","wikidata":"https://www.wikidata.org/wiki/Q833293","display_name":"Trapezoidal rule","level":3,"score":0.2906999886035919},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.2865000069141388},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.27889999747276306},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.2606000006198883},{"id":"https://openalex.org/C167590341","wikidata":"https://www.wikidata.org/wiki/Q5527850","display_name":"Gauss\u2013Hermite quadrature","level":5,"score":0.2551000118255615},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s0219876226500465","doi":"https://doi.org/10.1142/s0219876226500465","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s0219876226500465","pdf_url":null,"source":{"id":"https://openalex.org/S42084661","display_name":"International Journal of Computational Methods","issn_l":"0219-8762","issn":["0219-8762","1793-6969"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-c","jufo-1","norway-1","poland-70","russia-white-list-2"],"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computational Methods","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1422563354","display_name":null,"funder_award_id":"F.No. 16-9(June2018)/2019(NET/CSIR)","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G5127914553","display_name":null,"funder_award_id":"UGC-Ref. No. 999/(CSIR-UGC NET JUNE 2018)","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G76215917","display_name":null,"funder_award_id":"RUSA 2.0, T3A","funder_id":"https://openalex.org/F4320321573","funder_display_name":"Cochin University of Science and Technology"}],"funders":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"},{"id":"https://openalex.org/F4320321573","display_name":"Cochin University of Science and Technology","ror":"https://ror.org/00a4kqq17"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":37,"referenced_works":["https://openalex.org/W1963971605","https://openalex.org/W1980508838","https://openalex.org/W2001556612","https://openalex.org/W2005456640","https://openalex.org/W2006465918","https://openalex.org/W2011184843","https://openalex.org/W2016426644","https://openalex.org/W2019305020","https://openalex.org/W2036981510","https://openalex.org/W2038632102","https://openalex.org/W2040358792","https://openalex.org/W2044777272","https://openalex.org/W2050650133","https://openalex.org/W2057949621","https://openalex.org/W2060296485","https://openalex.org/W2072685235","https://openalex.org/W2077791698","https://openalex.org/W2081108726","https://openalex.org/W2091466745","https://openalex.org/W2097608413","https://openalex.org/W2103725449","https://openalex.org/W2108538926","https://openalex.org/W2111766677","https://openalex.org/W2138917657","https://openalex.org/W2144051128","https://openalex.org/W2146612430","https://openalex.org/W2154092206","https://openalex.org/W2584798035","https://openalex.org/W2609586384","https://openalex.org/W2908312441","https://openalex.org/W2950437334","https://openalex.org/W3007488135","https://openalex.org/W3013876872","https://openalex.org/W3164729664","https://openalex.org/W4214914074","https://openalex.org/W4297398298","https://openalex.org/W4298625112"],"related_works":[],"abstract_inverted_index":{"This":[0],"paper":[1],"presents":[2],"an":[3],"application":[4],"of":[5,20,53,78,89],"differential":[6,47,57],"quadrature":[7,48],"method":[8],"(DQM)":[9],"based":[10],"on":[11],"modified":[12],"cubic":[13],"B-splines":[14],"for":[15,75],"obtaining":[16],"the":[17,40,54,76,90],"numerical":[18,82],"solution":[19],"generalized":[21,25,66],"Black\u2013Scholes":[22,26],"equation.":[23],"The":[24,50,81],"equation":[27,35,58],"is":[28,43,61,92],"transformed":[29,41],"to":[30],"a":[31],"time":[32,51],"progressing":[33],"nondegenerate":[34],"by":[36],"logarithmic":[37],"transformation":[38],"and":[39,65,86],"model":[42],"spatially":[44],"discretized":[45],"using":[46],"method.":[49],"integration":[52],"corresponding":[55],"ordinary":[56],"(ODE)":[59],"system":[60,91],"executed":[62],"with":[63],"SSPRK54":[64],"trapezoidal":[67],"formula":[68],"(GTF).":[69],"Several":[70],"test":[71],"problems":[72],"are":[73,84],"examined":[74],"validation":[77],"theoretical":[79],"results.":[80],"experiments":[83],"compared":[85],"computational":[87],"stability":[88],"also":[93],"ensured.":[94]},"counts_by_year":[],"updated_date":"2026-10-09T09:14:12.587421","created_date":"2026-06-28T00:00:00"}