{"id":"https://openalex.org/W4408310685","doi":"https://doi.org/10.1142/s1793005726500523","title":"Newton Polynomial Collocation Method for Linear Differential Equations","display_name":"Newton Polynomial Collocation Method for Linear Differential Equations","publication_year":2025,"publication_date":"2025-03-11","ids":{"openalex":"https://openalex.org/W4408310685","doi":"https://doi.org/10.1142/s1793005726500523"},"language":"en","primary_location":{"id":"doi:10.1142/s1793005726500523","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005726500523","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"New Mathematics and Natural Computation","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/A5058782567","display_name":"K.Bharatha Devi","orcid":null},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Kiran Devi","raw_affiliation_strings":["Department of Mathematics, University of Delhi, Delhi 110007, India"],"raw_orcid":"https://orcid.org/0009-0001-7749-4307","affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Delhi, Delhi 110007, India","institution_ids":["https://openalex.org/I110166357"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057069342","display_name":"Suvankar Biswas","orcid":"https://orcid.org/0000-0002-3305-0130"},"institutions":[{"id":"https://openalex.org/I51969498","display_name":"Indira Gandhi National Open University","ror":"https://ror.org/02fzfx471","country_code":"IN","type":"education","lineage":["https://openalex.org/I51969498"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Suvankar Biswas","raw_affiliation_strings":["Discipline of Mathematics, School of Sciences, Indira Gandhi National Open University, New Delhi 110068, India"],"raw_orcid":"https://orcid.org/0000-0002-3305-0130","affiliations":[{"raw_affiliation_string":"Discipline of Mathematics, School of Sciences, Indira Gandhi National Open University, New Delhi 110068, India","institution_ids":["https://openalex.org/I51969498"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5057692836","display_name":"Gunjan Khurana","orcid":"https://orcid.org/0000-0002-0634-6577"},"institutions":[{"id":"https://openalex.org/I110166357","display_name":"University of Delhi","ror":"https://ror.org/04gzb2213","country_code":"IN","type":"education","lineage":["https://openalex.org/I110166357"]}],"countries":["IN"],"is_corresponding":false,"raw_author_name":"Gunjan Khurana","raw_affiliation_strings":["Department of Mathematics, I.P. College for Women, University of Delhi, Delhi 110054, India"],"raw_orcid":"https://orcid.org/0000-0002-0634-6577","affiliations":[{"raw_affiliation_string":"Department of Mathematics, I.P. College for Women, University of Delhi, Delhi 110054, India","institution_ids":["https://openalex.org/I110166357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"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":0.06505364,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"22","issue":"04","first_page":"1211","last_page":"1225"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9287999868392944,"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9287999868392944,"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/collocation-method","display_name":"Collocation method","score":0.6511209011077881},{"id":"https://openalex.org/keywords/orthogonal-collocation","display_name":"Orthogonal collocation","score":0.6353956460952759},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.606803834438324},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5725059509277344},{"id":"https://openalex.org/keywords/newtons-method","display_name":"Newton's method","score":0.5594162940979004},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5487995743751526},{"id":"https://openalex.org/keywords/collocation","display_name":"Collocation (remote sensing)","score":0.540347158908844},{"id":"https://openalex.org/keywords/linear-differential-equation","display_name":"Linear differential equation","score":0.42965278029441833},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.41813206672668457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38450855016708374},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.3103474974632263},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.30443310737609863},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.21106231212615967},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07902184128761292}],"concepts":[{"id":"https://openalex.org/C2126413","wikidata":"https://www.wikidata.org/wiki/Q1779479","display_name":"Collocation method","level":4,"score":0.6511209011077881},{"id":"https://openalex.org/C114609681","wikidata":"https://www.wikidata.org/wiki/Q24839227","display_name":"Orthogonal collocation","level":5,"score":0.6353956460952759},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.606803834438324},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5725059509277344},{"id":"https://openalex.org/C85189116","wikidata":"https://www.wikidata.org/wiki/Q374195","display_name":"Newton's method","level":3,"score":0.5594162940979004},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5487995743751526},{"id":"https://openalex.org/C80023036","wikidata":"https://www.wikidata.org/wiki/Q5147531","display_name":"Collocation (remote sensing)","level":2,"score":0.540347158908844},{"id":"https://openalex.org/C13982400","wikidata":"https://www.wikidata.org/wiki/Q1129902","display_name":"Linear differential equation","level":3,"score":0.42965278029441833},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.41813206672668457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38450855016708374},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.3103474974632263},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.30443310737609863},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.21106231212615967},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07902184128761292},{"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/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793005726500523","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793005726500523","pdf_url":null,"source":{"id":"https://openalex.org/S135331755","display_name":"New Mathematics and Natural Computation","issn_l":"1793-0057","issn":["1793-0057","1793-7027"],"is_oa":false,"is_in_doaj":false,"is_core":true,"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":"New Mathematics and Natural Computation","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":39,"referenced_works":["https://openalex.org/W1560556759","https://openalex.org/W1969202999","https://openalex.org/W1969742024","https://openalex.org/W1999052859","https://openalex.org/W2004382646","https://openalex.org/W2012004495","https://openalex.org/W2019807417","https://openalex.org/W2050435316","https://openalex.org/W2062550395","https://openalex.org/W2072203466","https://openalex.org/W2089857413","https://openalex.org/W2149993491","https://openalex.org/W2158985775","https://openalex.org/W2166855174","https://openalex.org/W2183007503","https://openalex.org/W2304687139","https://openalex.org/W2308953129","https://openalex.org/W2558664449","https://openalex.org/W3000189728","https://openalex.org/W3030090692","https://openalex.org/W3041754454","https://openalex.org/W3096143543","https://openalex.org/W3112730845","https://openalex.org/W3200651239","https://openalex.org/W4294904757","https://openalex.org/W4297817245","https://openalex.org/W4303444351","https://openalex.org/W4306631607","https://openalex.org/W4312201012","https://openalex.org/W4319844782","https://openalex.org/W4361295712","https://openalex.org/W4379380229","https://openalex.org/W4381620905","https://openalex.org/W4383814256","https://openalex.org/W4386700227","https://openalex.org/W4386785638","https://openalex.org/W4387307870","https://openalex.org/W4390747099","https://openalex.org/W4399891135"],"related_works":["https://openalex.org/W2791210196","https://openalex.org/W2078318892","https://openalex.org/W4255016916","https://openalex.org/W2111003632","https://openalex.org/W2889856026","https://openalex.org/W1987365920","https://openalex.org/W1989122168","https://openalex.org/W2150070385","https://openalex.org/W2000247808","https://openalex.org/W2384941625"],"abstract_inverted_index":{"Newton":[0,26,33],"polynomials":[1,27,34],"are":[2,105],"used":[3,37,54],"to":[4,20,38,58,63,92,114,148],"develop":[5],"a":[6,43,60,81],"collocation":[7,56],"method":[8,73],"for":[9,143],"the":[10,22,40,48,64,68,76,94,99,108,116,119,125,141,150],"first":[11],"time.":[12],"The":[13,45,71,102],"fundamental":[14],"idea":[15],"of":[16,47,67,83,98,110,118,146,152],"our":[17,153],"technique":[18],"is":[19],"estimate":[21],"solution":[23,41,66],"by":[24],"employing":[25],"and":[28,96,134],"collocating":[29],"at":[30,137],"Legendre-type":[31],"points.":[32],"have":[35,52,87,123],"been":[36,53],"approximate":[39],"as":[42,55],"series.":[44],"roots":[46],"Legendre":[49],"orthogonal":[50],"polynomial":[51],"points":[57,139],"ensure":[59],"closer":[61],"estimation":[62],"analytical":[65],"given":[69],"problem.":[70],"presented":[72,112],"brings":[74],"down":[75],"ordinary":[77],"differential":[78],"equation":[79],"into":[80],"set":[82],"algebraic":[84],"equations.":[85],"We":[86,122],"numerically":[88],"computed":[89],"several":[90],"examples":[91],"demonstrate":[93],"validity":[95],"applicability":[97],"proposed":[100,120],"method.":[101,154],"numerical":[103],"outcomes":[104],"collated":[106],"with":[107],"solutions":[109],"already":[111],"techniques":[113],"highlight":[115],"effectiveness":[117],"technique.":[121],"tabulated":[124],"absolute":[126,130],"point-wise":[127],"errors,":[128,131,133],"maximum":[129],"relative":[132],"reference":[135],"errors":[136],"different":[138,144],"in":[140],"domain":[142],"numbers":[145],"collocations":[147],"exhibit":[149],"convergence":[151]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
