{"id":"https://openalex.org/W4321113877","doi":"https://doi.org/10.1016/j.cam.2023.115127","title":"SODES: Solving ordinary differential equations step by step","display_name":"SODES: Solving ordinary differential equations step by step","publication_year":2023,"publication_date":"2023-02-16","ids":{"openalex":"https://openalex.org/W4321113877","doi":"https://doi.org/10.1016/j.cam.2023.115127"},"language":"en","primary_location":{"id":"doi:10.1016/j.cam.2023.115127","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cam.2023.115127","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://doi.org/10.1016/j.cam.2023.115127","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053400101","display_name":"Jos\u00e9 Luis Gal\u00e1n\u2013Garc\u00eda","orcid":"https://orcid.org/0000-0002-8773-6998"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Jos\u00e9 Luis Gal\u00e1n\u2013Garc\u00eda","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013666941","display_name":"Pedro Rodr\u00edguez\u2013Cielos","orcid":"https://orcid.org/0000-0003-1498-8841"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pedro Rodr\u00edguez\u2013Cielos","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082342030","display_name":"Mar\u00eda \u00c1ngeles Gal\u00e1n\u2013Garc\u00eda","orcid":"https://orcid.org/0000-0002-8906-3125"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Mar\u00eda \u00c1ngeles Gal\u00e1n\u2013Garc\u00eda","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051884852","display_name":"Morgan le Goff","orcid":null},"institutions":[{"id":"https://openalex.org/I198244214","display_name":"Universit\u00e9 Clermont Auvergne","ror":"https://ror.org/01a8ajp46","country_code":"FR","type":"education","lineage":["https://openalex.org/I198244214"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Morgan le Goff","raw_affiliation_strings":["G\u00e9nie Math\u00e9matiques et Mod\u00e9lisation. Polytech Clermont Ferrand Universit\u00e9 Clermont Auvergne, France"],"affiliations":[{"raw_affiliation_string":"G\u00e9nie Math\u00e9matiques et Mod\u00e9lisation. Polytech Clermont Ferrand Universit\u00e9 Clermont Auvergne, France","institution_ids":["https://openalex.org/I198244214"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066936588","display_name":"Yolanda Padilla\u2013Dom\u00ednguez","orcid":"https://orcid.org/0000-0001-7059-9897"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Yolanda Padilla\u2013Dom\u00ednguez","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077802441","display_name":"Pablo Rodr\u00edguez-Padilla","orcid":"https://orcid.org/0009-0000-7811-7645"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Pablo Rodr\u00edguez-Padilla","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007022701","display_name":"I. Atencia","orcid":"https://orcid.org/0000-0001-6131-2778"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Iv\u00e1n Atencia","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050402697","display_name":"Gabriel Aguilera\u2010Venegas","orcid":"https://orcid.org/0000-0002-5813-6184"},"institutions":[{"id":"https://openalex.org/I82767444","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28","country_code":"ES","type":"education","lineage":["https://openalex.org/I82767444"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Gabriel Aguilera\u2013Venegas","raw_affiliation_strings":["Department of Applied Mathematics. University of M\u00e1laga, Spain"],"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics. University of M\u00e1laga, Spain","institution_ids":["https://openalex.org/I82767444"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5053400101"],"corresponding_institution_ids":["https://openalex.org/I82767444"],"apc_list":{"value":3040,"currency":"USD","value_usd":3040},"apc_paid":{"value":3040,"currency":"USD","value_usd":3040},"fwci":0.5863,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69016328,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":96},"biblio":{"volume":"428","issue":null,"first_page":"115127","last_page":"115127"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9302999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12162","display_name":"Cellular Automata and Applications","score":0.9302999973297119,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9068999886512756,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.9184613227844238},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.6502009630203247},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.46743929386138916},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.42003750801086426},{"id":"https://openalex.org/keywords/l-stability","display_name":"L-stability","score":0.4124220013618469},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.38792556524276733},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.3553844094276428},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3525804877281189}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.9184613227844238},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6502009630203247},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.46743929386138916},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.42003750801086426},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.4124220013618469},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38792556524276733},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.3553844094276428},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3525804877281189},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1016/j.cam.2023.115127","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cam.2023.115127","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:riuma.uma.es:10630/26407","is_oa":true,"landing_page_url":"https://hdl.handle.net/10630/26407","pdf_url":"https://riuma.uma.es/xmlui/bitstream/10630/26407/1/1-s2.0-S0377042723000717-main.pdf","source":{"id":"https://openalex.org/S4306401385","display_name":"Repositorio Institucional de la Universidad de M\u00e1laga (University of M\u00e1laga)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I82767444","host_organization_name":"Universidad de M\u00e1laga","host_organization_lineage":["https://openalex.org/I82767444"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"VoR"}],"best_oa_location":{"id":"doi:10.1016/j.cam.2023.115127","is_oa":true,"landing_page_url":"https://doi.org/10.1016/j.cam.2023.115127","pdf_url":null,"source":{"id":"https://openalex.org/S165473669","display_name":"Journal of Computational and Applied Mathematics","issn_l":"0377-0427","issn":["0377-0427","1879-1778"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320990","host_organization_name":"Elsevier BV","host_organization_lineage":["https://openalex.org/P4310320990"],"host_organization_lineage_names":["Elsevier BV"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Computational and Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[{"score":0.7200000286102295,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320311265","display_name":"Universidad de M\u00e1laga","ror":"https://ror.org/036b2ww28"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1846027651","https://openalex.org/W1966138133","https://openalex.org/W1998329334","https://openalex.org/W2004720904","https://openalex.org/W2030388743","https://openalex.org/W2051093092","https://openalex.org/W2056555906","https://openalex.org/W2081497310","https://openalex.org/W2090836551","https://openalex.org/W2170579767","https://openalex.org/W2282592301","https://openalex.org/W2311401672","https://openalex.org/W2561509960","https://openalex.org/W2911674122","https://openalex.org/W2937787624","https://openalex.org/W2946544204","https://openalex.org/W3213007371","https://openalex.org/W4210534911","https://openalex.org/W4249835868","https://openalex.org/W6650013039"],"related_works":["https://openalex.org/W2187470707","https://openalex.org/W2286595471","https://openalex.org/W3195608350","https://openalex.org/W2463263167","https://openalex.org/W2049253768","https://openalex.org/W1569440961","https://openalex.org/W2188598241","https://openalex.org/W2016501519","https://openalex.org/W2043671984","https://openalex.org/W3021188244"],"abstract_inverted_index":{"In":[0,185],"this":[1,186],"paper,":[2],"we":[3,75,188],"introduce":[4,191],"SODES":[5,19,35,62,92,164,201,245],"(Stepwise":[6],"Ordinary":[7,15],"Differential":[8,16],"Equations":[9,17],"Solver)":[10],"a":[11,69,178,192,195,203,218],"new":[12],"solver":[13],"for":[14,42,54,135,200],"(ODE).":[18],"can":[20,82,226,235,255],"optionally":[21],"provide":[22],"the":[23,27,55,77,97,100,173,183,247],"solution":[24,98],"displaying":[25],"all":[26],"steps":[28],"needed":[29],"to":[30,86,239,265,268],"obtain":[31],"it.":[32],"This":[33,224],"way,":[34],"is":[36,217],"an":[37,51],"important":[38,52],"tool":[39,53],"not":[40],"only":[41],"researchers":[43],"who":[44,260],"need":[45],"solving":[46],"ODE":[47,115,180],"but":[48,80],"also":[49,165,190,261],"constitutes":[50],"teaching":[56],"and":[57,153,181,221,232,234,246],"learning":[58],"process":[59],"of":[60,99,103,116,121,138,156,177,194,244],"ODE.":[61],"has":[63],"been":[64],"developed":[65],"using":[66,207],"programming":[67,208],"with":[68,130,143,150,161,167],"Computer":[70],"Algebra":[71],"System":[72],"(CAS).":[73],"Specifically,":[74],"use":[76],"CAS":[78,89,213],"Derive":[79],"it":[81,254,267],"be":[83,227,236,256,263],"easily":[84,237],"adapted":[85],"any":[87],"other":[88,240],"supporting":[90],"programming.":[91],"provides,":[93],"step":[94],"by":[95,258],"step,":[96],"following":[101],"types":[102,176],"ODE:":[104],"separable,":[105],"homogeneous,":[106],"exact,":[107],"integrating":[108],"factors,":[109],"linear,":[110],"Bernoulli,":[111],"Riccati,":[112],"first":[113,122],"order":[114,123,126,140,147,158],"nth":[117],"degree,":[118],"Cauchy\u2019s":[119,154],"problems":[120,155],"ODE,":[124],"higher":[125,139,146,157],"linear":[127,141,148,159],"homogeneous":[128],"equations":[129,142,149,160],"constant":[131,144,151,162],"coefficients,":[132,145],"Lagrange\u2019s":[133],"method":[134],"particular":[136],"solutions":[137],"coefficients":[152],"coefficients.":[163],"deals":[166],"two":[168],"generic":[169],"programs":[170],"which":[171,216],"determine":[172],"type":[174],"or":[175],"given":[179],"provides":[182],"solution.":[184],"paper":[187],"will":[189,262],"draft":[193,225],"Graphical":[196],"User":[197],"Interface":[198],"(GUI)":[199],"in":[202,209,229],"local":[204],"web":[205],"application":[206],"Python":[210],"(using":[211],"its":[212],"module":[214],"SymPy)":[215],"more":[219],"portable":[220],"free":[222],"CAS.":[223],"used":[228,257],"English,":[230],"French":[231],"Spanish,":[233],"extended":[238],"languages.":[241],"The":[242],"code":[243],"GUI":[248],"are":[249],"freely":[250],"available":[251],"so":[252],"that":[253],"users":[259],"able":[264],"adapt":[266],"their":[269],"needs.":[270]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-04-16T15:07:20.185449","created_date":"2025-10-10T00:00:00"}
