{"id":"https://openalex.org/W2062568129","doi":"https://doi.org/10.1137/0914053","title":"Optimizing the Numerical Integration of Initial Value Problems in Shooting Methods for Linear Boundary Value Problems","display_name":"Optimizing the Numerical Integration of Initial Value Problems in Shooting Methods for Linear Boundary Value Problems","publication_year":1993,"publication_date":"1993-07-01","ids":{"openalex":"https://openalex.org/W2062568129","doi":"https://doi.org/10.1137/0914053","mag":"2062568129"},"language":"en","primary_location":{"id":"doi:10.1137/0914053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914053","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","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/A5083672564","display_name":"L. R\u00e1ndez","orcid":"https://orcid.org/0000-0002-4238-3228"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"L. R\u00e1ndez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5083672564"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.23859649,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"14","issue":"4","first_page":"860","last_page":"871"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9991000294685364,"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":0.9991000294685364,"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":0.989300012588501,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8480642437934875},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.6877991557121277},{"id":"https://openalex.org/keywords/ode","display_name":"Ode","score":0.6343940496444702},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.5494680404663086},{"id":"https://openalex.org/keywords/shooting-method","display_name":"Shooting method","score":0.5481640100479126},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5466899275779724},{"id":"https://openalex.org/keywords/truncation","display_name":"Truncation (statistics)","score":0.5375219583511353},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5174587368965149},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.5035557150840759},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4994380474090576},{"id":"https://openalex.org/keywords/boundary-value-problem","display_name":"Boundary value problem","score":0.4863191545009613},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4127596616744995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36997103691101074},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3690134882926941},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1315022110939026}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8480642437934875},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.6877991557121277},{"id":"https://openalex.org/C34862557","wikidata":"https://www.wikidata.org/wiki/Q178985","display_name":"Ode","level":2,"score":0.6343940496444702},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.5494680404663086},{"id":"https://openalex.org/C4195266","wikidata":"https://www.wikidata.org/wiki/Q1749769","display_name":"Shooting method","level":3,"score":0.5481640100479126},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5466899275779724},{"id":"https://openalex.org/C106195933","wikidata":"https://www.wikidata.org/wiki/Q7847935","display_name":"Truncation (statistics)","level":2,"score":0.5375219583511353},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5174587368965149},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.5035557150840759},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4994380474090576},{"id":"https://openalex.org/C182310444","wikidata":"https://www.wikidata.org/wiki/Q1332643","display_name":"Boundary value problem","level":2,"score":0.4863191545009613},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4127596616744995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36997103691101074},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3690134882926941},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1315022110939026},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1137/0914053","is_oa":false,"landing_page_url":"https://doi.org/10.1137/0914053","pdf_url":null,"source":{"id":"https://openalex.org/S165512578","display_name":"SIAM Journal on Scientific Computing","issn_l":"1064-8275","issn":["1064-8275","1095-7197"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320306101","display_name":"National Aeronautics and Space Administration","ror":"https://ror.org/027ka1x80"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W1966586124","https://openalex.org/W1969402770","https://openalex.org/W1987456624","https://openalex.org/W2000397373","https://openalex.org/W2008542229","https://openalex.org/W2012780794","https://openalex.org/W2019230842","https://openalex.org/W2061376823","https://openalex.org/W2066979198","https://openalex.org/W2075655265","https://openalex.org/W2809460247","https://openalex.org/W4300831536"],"related_works":["https://openalex.org/W1996389252","https://openalex.org/W138907054","https://openalex.org/W2931873406","https://openalex.org/W21086365","https://openalex.org/W2040666836","https://openalex.org/W2238041693","https://openalex.org/W2112774109","https://openalex.org/W125347959","https://openalex.org/W2044869171","https://openalex.org/W1998311370"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"two":[3],"new":[4],"embedded":[5],"Runge-Kutta":[6],"(RK)":[7],"methods":[8],"RK5(4)":[9],"specially":[10],"designed":[11],"for":[12],"linear":[13],"ODEs":[14],"[L.":[15],"F.":[16],"Shampine,":[17],"J.":[18,76],"Comput.":[19],"Appl.":[20],"Math.,":[21],"15":[22],"(1986),":[23],"pp.":[24,81],"293\u2013300]":[25],"are":[26,83],"derived":[27],"with":[28,64],"(a)":[29],"\u201csmall\u201d":[30],"principal":[31],"truncation":[32],"terms":[33],"in":[34],"the":[35,54,65],"fifth-order":[36],"formula,":[37],"and":[38,71],"(b)":[39],"minimum":[40],"number":[41],"of":[42],"Jacobian":[43],"matrix":[44],"evaluations":[45],"per":[46],"step.":[47],"Numerical":[48],"tests":[49],"comparing":[50],"their":[51],"efficiency":[52],"to":[53],"classical":[55],"RKF5(4)#2":[56],"[E.":[57],"Fehlberg,":[58],"Tech.":[59],"Rep.":[60],"R-315,":[61],"NASA,":[62],"1969],":[63],"SUPORT":[66],"code":[67],"[M.":[68],"R.":[69],"Scott":[70],"H.":[72],"A.":[73],"Watts,":[74],"SIAM":[75],"Nmmer.":[77],"Anal.,":[78],"1":[79],"(1977),":[80],"40\u201370],":[82],"presented.":[84]},"counts_by_year":[],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}