{"id":"https://openalex.org/W4404776010","doi":"https://doi.org/10.1155/cmm4/7393931","title":"Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method","display_name":"Approximate Solution of an Integrodifferential Equation Generalized by Harry Dym Equation Using the Picard Successive Method","publication_year":2024,"publication_date":"2024-01-01","ids":{"openalex":"https://openalex.org/W4404776010","doi":"https://doi.org/10.1155/cmm4/7393931"},"language":"en","primary_location":{"id":"doi:10.1155/cmm4/7393931","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cmm4/7393931","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cmm4/7393931","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cmm4/7393931","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5000398391","display_name":"Rabeea Mohammed Hani Darghoth","orcid":"https://orcid.org/0000-0002-1435-5780"},"institutions":[{"id":"https://openalex.org/I12150220","display_name":"University of Mosul","ror":"https://ror.org/039cf4q47","country_code":"IQ","type":"education","lineage":["https://openalex.org/I12150220"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Rabeea Mohammed Hani Darghoth","raw_affiliation_strings":["Department of Mathematics ,  College of Basic Education ,  University of Mosul ,  Mosul ,  Iraq , uomosul.edu.iq"],"raw_orcid":"https://orcid.org/0000-0002-1435-5780","affiliations":[{"raw_affiliation_string":"Department of Mathematics ,  College of Basic Education ,  University of Mosul ,  Mosul ,  Iraq , uomosul.edu.iq","institution_ids":["https://openalex.org/I12150220"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5000398391"],"corresponding_institution_ids":["https://openalex.org/I12150220"],"apc_list":{"value":750,"currency":"USD","value_usd":750},"apc_paid":{"value":750,"currency":"USD","value_usd":750},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.21461227,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2024","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9933000206947327,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9919000267982483,"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":0.6132505536079407},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.413014680147171},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.37925782799720764},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3529685139656067},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.06000781059265137}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6132505536079407},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.413014680147171},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.37925782799720764},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3529685139656067},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06000781059265137},{"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:10.1155/cmm4/7393931","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cmm4/7393931","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cmm4/7393931","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:5667b56a4b0b40e28fc16e8dbc97e654","is_oa":true,"landing_page_url":"https://doaj.org/article/5667b56a4b0b40e28fc16e8dbc97e654","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Computational and Mathematical Methods, Vol 2024 (2024)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/cmm4/7393931","is_oa":true,"landing_page_url":"https://doi.org/10.1155/cmm4/7393931","pdf_url":"https://onlinelibrary.wiley.com/doi/pdfdirect/10.1155/cmm4/7393931","source":{"id":"https://openalex.org/S4210240678","display_name":"Computational and Mathematical Methods","issn_l":"2577-7408","issn":["2577-7408"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Computational and Mathematical Methods","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320318976","display_name":"University of Mosul","ror":"https://ror.org/039cf4q47"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4404776010.pdf"},"referenced_works_count":16,"referenced_works":["https://openalex.org/W1573376668","https://openalex.org/W2005432145","https://openalex.org/W2009541277","https://openalex.org/W2009804095","https://openalex.org/W2010319345","https://openalex.org/W2020204532","https://openalex.org/W2053901883","https://openalex.org/W2148571448","https://openalex.org/W2171590375","https://openalex.org/W2891161821","https://openalex.org/W2946717497","https://openalex.org/W3014722153","https://openalex.org/W3167534489","https://openalex.org/W4308008108","https://openalex.org/W4384933491","https://openalex.org/W4399296069"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W2142036596","https://openalex.org/W2072657027","https://openalex.org/W2962838298","https://openalex.org/W2600246793"],"abstract_inverted_index":{"In":[0],"this":[1,68],"study,":[2],"we":[3,33],"discuss":[4],"the":[5,9,23,28,39,46,62,75,78,88,92,95],"approximate":[6,40,53],"solution":[7,41,90],"of":[8,38,45,61,67,77,94],"Harry":[10,48],"Dym":[11,49],"nonlinear":[12],"partial":[13,47],"differential":[14],"equation":[15],"and":[16],"its":[17],"integrodifferential":[18,50],"version.":[19],"We":[20],"first":[21],"construct":[22],"Picard":[24],"successive":[25],"approximation":[26],"for":[27,42,57],"equations":[29],"under":[30],"consideration.":[31],"Then,":[32],"give":[34],"a":[35],"detailed":[36],"calculation":[37],"two":[43],"cases":[44],"equation.":[51],"The":[52,65],"solutions":[54],"are":[55],"illustrated":[56],"some":[58],"chosen":[59],"values":[60],"arbitrary":[63],"constants.":[64],"efficiency":[66],"semianalytical":[69],"method":[70],"is":[71],"demonstrated":[72],"through":[73],"discussing":[74],"regions":[76],"domain":[79],"with":[80],"small":[81],"errors":[82],"as":[83,85],"well":[84],"by":[86],"extracting":[87],"exact":[89],"from":[91],"limit":[93],"approximation.":[96]},"counts_by_year":[],"updated_date":"2026-06-14T07:44:22.658603","created_date":"2025-10-10T00:00:00"}
