{"id":"https://openalex.org/W2066319239","doi":"https://doi.org/10.1080/0020716031000112358","title":"On the Convergence of Finite Difference Method for General Singular Boundary Value Problems","display_name":"On the Convergence of Finite Difference Method for General Singular Boundary Value Problems","publication_year":2003,"publication_date":"2003-10-01","ids":{"openalex":"https://openalex.org/W2066319239","doi":"https://doi.org/10.1080/0020716031000112358","mag":"2066319239"},"language":"en","primary_location":{"id":"doi:10.1080/0020716031000112358","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020716031000112358","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"],"host_organization_lineage_names":["Taylor & Francis"],"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/A5101630479","display_name":"R.K. Pandey","orcid":"https://orcid.org/0000-0003-1216-0282"},"institutions":[{"id":"https://openalex.org/I4210153001","display_name":"North-West State Technical University","ror":"https://ror.org/04dm8yx03","country_code":"RU","type":"education","lineage":["https://openalex.org/I4210153001"]}],"countries":["RU"],"is_corresponding":true,"raw_author_name":"R. K. Pandey","raw_affiliation_strings":["Correspondencerkp64@satyam.net.in"],"affiliations":[{"raw_affiliation_string":"Correspondencerkp64@satyam.net.in","institution_ids":["https://openalex.org/I4210153001"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101511265","display_name":"Arvind Kumar Singh","orcid":"https://orcid.org/0000-0001-6162-5870"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Arvind K. Singh","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5101630479"],"corresponding_institution_ids":["https://openalex.org/I4210153001"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.17648818,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"80","issue":"10","first_page":"1323","last_page":"1331"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9991999864578247,"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":0.9991999864578247,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9968000054359436,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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":0.9925000071525574,"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":0.8049249649047852},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.661115288734436},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.6217060089111328},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5301324725151062},{"id":"https://openalex.org/keywords/boundary","display_name":"Boundary (topology)","score":0.5270341038703918},{"id":"https://openalex.org/keywords/singular-point-of-a-curve","display_name":"Singular point of a curve","score":0.48362839221954346},{"id":"https://openalex.org/keywords/singular-boundary-method","display_name":"Singular boundary method","score":0.4826570153236389},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.47204363346099854},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4349581301212311},{"id":"https://openalex.org/keywords/singular-value","display_name":"Singular value","score":0.4272807240486145},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.4245338439941406},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.41843512654304504},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3445996046066284},{"id":"https://openalex.org/keywords/finite-element-method","display_name":"Finite element method","score":0.1796453595161438},{"id":"https://openalex.org/keywords/boundary-element-method","display_name":"Boundary element method","score":0.12835893034934998},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.07125502824783325},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06428709626197815}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8049249649047852},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.661115288734436},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6217060089111328},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5301324725151062},{"id":"https://openalex.org/C62354387","wikidata":"https://www.wikidata.org/wiki/Q875399","display_name":"Boundary (topology)","level":2,"score":0.5270341038703918},{"id":"https://openalex.org/C200917960","wikidata":"https://www.wikidata.org/wiki/Q3847057","display_name":"Singular point of a curve","level":2,"score":0.48362839221954346},{"id":"https://openalex.org/C82047721","wikidata":"https://www.wikidata.org/wiki/Q7524247","display_name":"Singular boundary method","level":4,"score":0.4826570153236389},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.47204363346099854},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4349581301212311},{"id":"https://openalex.org/C109282560","wikidata":"https://www.wikidata.org/wiki/Q4166054","display_name":"Singular value","level":3,"score":0.4272807240486145},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.4245338439941406},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.41843512654304504},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3445996046066284},{"id":"https://openalex.org/C135628077","wikidata":"https://www.wikidata.org/wiki/Q220184","display_name":"Finite element method","level":2,"score":0.1796453595161438},{"id":"https://openalex.org/C63632240","wikidata":"https://www.wikidata.org/wiki/Q1935004","display_name":"Boundary element method","level":3,"score":0.12835893034934998},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.07125502824783325},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06428709626197815},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C31258907","wikidata":"https://www.wikidata.org/wiki/Q1301371","display_name":"Computer network","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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","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},{"id":"https://openalex.org/C127162648","wikidata":"https://www.wikidata.org/wiki/Q16858953","display_name":"Channel (broadcasting)","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/0020716031000112358","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020716031000112358","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"],"host_organization_lineage_names":["Taylor & Francis"],"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":11,"referenced_works":["https://openalex.org/W1969281124","https://openalex.org/W1971657634","https://openalex.org/W1996986887","https://openalex.org/W2013446180","https://openalex.org/W2014646453","https://openalex.org/W2023128601","https://openalex.org/W2038973894","https://openalex.org/W2048923395","https://openalex.org/W2056792813","https://openalex.org/W2070127486","https://openalex.org/W2093442265"],"related_works":["https://openalex.org/W2365193650","https://openalex.org/W1556508989","https://openalex.org/W2359963295","https://openalex.org/W2094931821","https://openalex.org/W1973423023","https://openalex.org/W4206452777","https://openalex.org/W2133117857","https://openalex.org/W2054819197","https://openalex.org/W2012917162","https://openalex.org/W4368368567"],"abstract_inverted_index":{"Abstract":[0],"The":[1],"finite":[2],"difference":[3,108],"method":[4,80,109],"M3":[5],"developed":[6],"in":[7],"Ref.":[8],"Citation[4]":[9],"by":[10,115],"Chawla":[11],"and":[12,34,71,119,124],"Katti":[13],"for":[14,50,84,90],"singular":[15,52,105],"two":[16],"point":[17,104],"boundary":[18,35,53,73],"value":[19,54],"problems":[20,55],"with":[21,56],"p(x)":[22,59,93],"=":[23,38,41,60],"x":[24,61],"b":[25,30,62,67],"0":[26,28,31,63,65,68],",":[27],"\u2264":[29,66],"<":[32,69],"1":[33,70],"conditions":[36,74],"y(0)":[37],"A,":[39],"y(1)":[40],"B":[42,44],"(A,":[43],"are":[45],"constants)":[46],"has":[47,81],"been":[48,82],"extended":[49],"the":[51,72,79,95,100],"general":[57,86,91],"function":[58,92],"g(x),":[64],"Second":[75],"order":[76,96],"convergence":[77,98],"of":[78,97,99,117],"established":[83],"quite":[85],"conditions.":[87],"Numerical":[88],"examples":[89],"verify":[94],"method.":[101],"Keywords:":[102],"2":[103],"B.V.":[106],"problemsFinite":[107],"Acknowlegement":[110],"This":[111],"work":[112],"is":[113],"supported":[114],"Department":[116],"Science":[118],"Technology,":[120],"New":[121,126],"Delhi,":[122,127],"India":[123],"CSIR,":[125],"India.":[128]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2016,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
