{"id":"https://openalex.org/W4323043671","doi":"https://doi.org/10.3390/sym15030631","title":"New Numerical Methods for Solving the Initial Value Problem Based on a Symmetrical Quadrature Integration Formula Using Hybrid Functions","display_name":"New Numerical Methods for Solving the Initial Value Problem Based on a Symmetrical Quadrature Integration Formula Using Hybrid Functions","publication_year":2023,"publication_date":"2023-03-02","ids":{"openalex":"https://openalex.org/W4323043671","doi":"https://doi.org/10.3390/sym15030631"},"language":"en","primary_location":{"id":"doi:10.3390/sym15030631","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030631","pdf_url":"https://www.mdpi.com/2073-8994/15/3/631/pdf?version=1678070693","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/15/3/631/pdf?version=1678070693","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5010147825","display_name":"Zainab J. Kadum","orcid":null},"institutions":[{"id":"https://openalex.org/I126633494","display_name":"University of Basrah","ror":"https://ror.org/00840ea57","country_code":"IQ","type":"education","lineage":["https://openalex.org/I126633494"]}],"countries":["IQ"],"is_corresponding":false,"raw_author_name":"Zainab J. Kadum","raw_affiliation_strings":["Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq","institution_ids":["https://openalex.org/I126633494"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014612319","display_name":"Noori Yasir Abdul-Hassan","orcid":"https://orcid.org/0000-0003-0621-4467"},"institutions":[{"id":"https://openalex.org/I126633494","display_name":"University of Basrah","ror":"https://ror.org/00840ea57","country_code":"IQ","type":"education","lineage":["https://openalex.org/I126633494"]}],"countries":["IQ"],"is_corresponding":true,"raw_author_name":"Noori Y. Abdul-Hassan","raw_affiliation_strings":["Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Education for Pure Sciences, University of Basrah, Basrah 61001, Iraq","institution_ids":["https://openalex.org/I126633494"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5014612319"],"corresponding_institution_ids":["https://openalex.org/I126633494"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2227},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2227},"fwci":3.3569,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.92751563,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"15","issue":"3","first_page":"631","last_page":"631"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9986000061035156,"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":0.9986000061035156,"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":0.9968000054359436,"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/T10288","display_name":"Fractional Differential Equations Solutions","score":0.9925000071525574,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.7993502616882324},{"id":"https://openalex.org/keywords/classification-of-discontinuities","display_name":"Classification of discontinuities","score":0.7538442611694336},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.6315130591392517},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5622704029083252},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.538941502571106},{"id":"https://openalex.org/keywords/nystr\u00f6m-method","display_name":"Nystr\u00f6m method","score":0.5262638330459595},{"id":"https://openalex.org/keywords/gravitational-singularity","display_name":"Gravitational singularity","score":0.5183485746383667},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.5085436105728149},{"id":"https://openalex.org/keywords/tanh-sinh-quadrature","display_name":"Tanh-sinh quadrature","score":0.5060383677482605},{"id":"https://openalex.org/keywords/gauss\u2013kronrod-quadrature-formula","display_name":"Gauss\u2013Kronrod quadrature formula","score":0.4997434616088867},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.476900577545166},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.4628185033798218},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4591367542743683},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"Initial value problem","score":0.4587095379829407},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.45349299907684326},{"id":"https://openalex.org/keywords/gaussian-quadrature","display_name":"Gaussian quadrature","score":0.41639912128448486},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.34779149293899536},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.3196883797645569},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2602859139442444},{"id":"https://openalex.org/keywords/integral-equation","display_name":"Integral equation","score":0.25184959173202515}],"concepts":[{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.7993502616882324},{"id":"https://openalex.org/C15627037","wikidata":"https://www.wikidata.org/wiki/Q541961","display_name":"Classification of discontinuities","level":2,"score":0.7538442611694336},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.6315130591392517},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5622704029083252},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.538941502571106},{"id":"https://openalex.org/C48265008","wikidata":"https://www.wikidata.org/wiki/Q7071295","display_name":"Nystr\u00f6m method","level":3,"score":0.5262638330459595},{"id":"https://openalex.org/C12843","wikidata":"https://www.wikidata.org/wiki/Q201721","display_name":"Gravitational singularity","level":2,"score":0.5183485746383667},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.5085436105728149},{"id":"https://openalex.org/C162046254","wikidata":"https://www.wikidata.org/wiki/Q7683194","display_name":"Tanh-sinh quadrature","level":5,"score":0.5060383677482605},{"id":"https://openalex.org/C14103991","wikidata":"https://www.wikidata.org/wiki/Q5527852","display_name":"Gauss\u2013Kronrod quadrature formula","level":4,"score":0.4997434616088867},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.476900577545166},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.4628185033798218},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4591367542743683},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.4587095379829407},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.45349299907684326},{"id":"https://openalex.org/C167196314","wikidata":"https://www.wikidata.org/wiki/Q767680","display_name":"Gaussian quadrature","level":4,"score":0.41639912128448486},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.34779149293899536},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.3196883797645569},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2602859139442444},{"id":"https://openalex.org/C27016315","wikidata":"https://www.wikidata.org/wiki/Q580101","display_name":"Integral equation","level":2,"score":0.25184959173202515},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym15030631","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030631","pdf_url":"https://www.mdpi.com/2073-8994/15/3/631/pdf?version=1678070693","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:867c6349fbfa4a6f86d0e275e0cf9e69","is_oa":false,"landing_page_url":"https://doaj.org/article/867c6349fbfa4a6f86d0e275e0cf9e69","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 15, Iss 3, p 631 (2023)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/15/3/631/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym15030631","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym15030631","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym15030631","pdf_url":"https://www.mdpi.com/2073-8994/15/3/631/pdf?version=1678070693","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4323043671.pdf"},"referenced_works_count":18,"referenced_works":["https://openalex.org/W2001786567","https://openalex.org/W2054987618","https://openalex.org/W2091837912","https://openalex.org/W2181621373","https://openalex.org/W2434540460","https://openalex.org/W2550092980","https://openalex.org/W2607425286","https://openalex.org/W2887130266","https://openalex.org/W2963874838","https://openalex.org/W3009947096","https://openalex.org/W3085442581","https://openalex.org/W3092618167","https://openalex.org/W4312352307","https://openalex.org/W4404665315","https://openalex.org/W6685818871","https://openalex.org/W6753763067","https://openalex.org/W6774359933","https://openalex.org/W6784438743"],"related_works":["https://openalex.org/W4387847482","https://openalex.org/W4390128132","https://openalex.org/W4377005030","https://openalex.org/W2012929093","https://openalex.org/W2148120208","https://openalex.org/W3154913590","https://openalex.org/W2049479394","https://openalex.org/W2550867510","https://openalex.org/W4317584040","https://openalex.org/W4205354206"],"abstract_inverted_index":{"In":[0],"this":[1],"study,":[2],"we":[3,83,121],"construct":[4],"new":[5],"numerical":[6,66,124],"methods":[7,31,58,95],"for":[8,47],"solving":[9],"the":[10,56,62,76,85,115,118,128],"initial":[11],"value":[12],"problem":[13],"(IVP)":[14],"in":[15],"ordinary":[16],"differential":[17],"equations":[18],"based":[19],"on":[20],"a":[21,98],"symmetrical":[22],"quadrature":[23],"integration":[24],"formula":[25],"using":[26],"hybrid":[27,80],"functions.":[28,81],"The":[29,52,93],"proposed":[30,57,119],"are":[32,44],"designed":[33],"to":[34,41,60,113,126],"provide":[35,122],"an":[36],"efficient":[37],"and":[38,43,71,87,108,130],"accurate":[39],"solution":[40],"IVP":[42],"more":[45],"suitable":[46],"problems":[48],"with":[49,75,105],"non-smooth":[50,110],"solutions.":[51],"key":[53],"idea":[54],"behind":[55],"is":[59],"combine":[61],"advantages":[63],"of":[64,78,90,101,117,132],"traditional":[65],"methods,":[67,74,120],"such":[68],"as":[69],"Runge\u2013Kutta":[70],"Taylor\u2019s":[72],"series":[73],"strengths":[77],"modern":[79],"Furthermore,":[82],"discuss":[84],"accuracy":[86,131],"stability":[88],"analysis":[89],"these":[91,133],"methods.":[92,134],"resulting":[94],"can":[96],"handle":[97],"wide":[99],"range":[100],"problems,":[102],"including":[103],"those":[104],"singularities,":[106],"discontinuities,":[107],"other":[109],"features.":[111],"Finally,":[112],"demonstrate":[114],"validity":[116],"several":[123],"examples":[125],"illustrate":[127],"efficiency":[129]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":5}],"updated_date":"2026-07-22T07:51:19.307946","created_date":"2025-10-10T00:00:00"}