{"id":"https://openalex.org/W7208815958","doi":"https://doi.org/10.62762/jam.2026.326643","title":"A Modified Third-Order Block Numerical Integration Technique for First Order Stiff and Oscillatory Differential Equations","display_name":"A Modified Third-Order Block Numerical Integration Technique for First Order Stiff and Oscillatory Differential Equations","publication_year":2026,"publication_date":"2026-09-04","ids":{"openalex":"https://openalex.org/W7208815958","doi":"https://doi.org/10.62762/jam.2026.326643"},"language":"en","primary_location":{"id":"doi:10.62762/jam.2026.326643","doi":"https://doi.org/10.62762/jam.2026.326643","is_oa":true,"landing_page_url":"https://doi.org/10.62762/jam.2026.326643","pdf_url":"https://www.icck.org/filebob/uploads/storage/JAM_uSKoruGy1SNCqriQk.pdf","source":{"id":"https://openalex.org/S5407049002","display_name":"ICCK Journal of Applied Mathematics","issn_l":"3068-5656","issn":["3068-5656"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICCK Journal of Applied Mathematics","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.icck.org/filebob/uploads/storage/JAM_uSKoruGy1SNCqriQk.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5159894002","display_name":"Abdulrahman Adamu","orcid":"https://orcid.org/0009-0002-7331-568X","observed_orcids":["https://orcid.org/0009-0002-7331-568X"]},"institutions":[{"id":"https://openalex.org/I4210147342","display_name":"Al-Qalam University Katsina","ror":"https://ror.org/04fmgc680","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210147342"]}],"countries":["NG"],"is_corresponding":true,"raw_author_name":"Abdulrahman Adamu","raw_affiliation_strings":["Department of Mathematics and Statistics, Al-Qalam University Katsina, Katsina State, Nigeria"],"raw_orcid":"https://orcid.org/0009-0002-7331-568X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Al-Qalam University Katsina, Katsina State, Nigeria","institution_ids":["https://openalex.org/I4210147342"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5146406119","display_name":"Buhari Alhassan","orcid":"https://orcid.org/0009-0006-5036-3696","observed_orcids":["https://orcid.org/0009-0006-5036-3696"]},"institutions":[{"id":"https://openalex.org/I4210147342","display_name":"Al-Qalam University Katsina","ror":"https://ror.org/04fmgc680","country_code":"NG","type":"education","lineage":["https://openalex.org/I4210147342"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Buhari Alhassan","raw_affiliation_strings":["Department of Mathematics and Statistics, Al-Qalam University Katsina, Katsina State, Nigeria"],"raw_orcid":"https://orcid.org/0009-0006-5036-3696","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics, Al-Qalam University Katsina, Katsina State, Nigeria","institution_ids":["https://openalex.org/I4210147342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5159894002"],"corresponding_institution_ids":["https://openalex.org/I4210147342"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"2","issue":"3","first_page":"242","last_page":"250"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical Solvers for Ordinary Differential Equations","score":0.9994999766349792,"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 Solvers for Ordinary Differential Equations","score":0.9994999766349792,"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":"Singular Perturbation, Asymptotics and Difference Schemes","score":9.999999747378752e-05,"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/T11191","display_name":"Mathematical functions and polynomials","score":9.999999747378752e-05,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stiff-differential-equations","display_name":"stiff ordinary differential equations","score":0.8650000095367432},{"id":"https://openalex.org/keywords/oscillatory-differential-equations","display_name":"oscillatory differential equations","score":0.9649999737739563},{"id":"https://openalex.org/keywords/a-stability","display_name":"A-stability","score":0.718999981880188},{"id":"https://openalex.org/keywords/zero-stability","display_name":"zero stability","score":0.6769999861717224},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.6690000295639038},{"id":"https://openalex.org/keywords/third-order-accuracy","display_name":"third-order accuracy","score":0.671999990940094},{"id":"https://openalex.org/keywords/initial-value-problem","display_name":"initial value problems","score":0.6970000267028809}],"concepts":[{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.7402999997138977},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7400000095367432},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.67330002784729},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.616599977016449},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.6093999743461609},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5666000247001648},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.5591999888420105},{"id":"https://openalex.org/C26955809","wikidata":"https://www.wikidata.org/wiki/Q10167591","display_name":"Initial value problem","level":2,"score":0.5151000022888184},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4964999854564667},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C43012357","wikidata":"https://www.wikidata.org/wiki/Q29744","display_name":"Stiff equation","level":3,"score":0.4828999936580658},{"id":"https://openalex.org/C149393637","wikidata":"https://www.wikidata.org/wiki/Q5421265","display_name":"Explicit and implicit methods","level":5,"score":0.41780000925064087},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.4122999906539917},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.40149998664855957},{"id":"https://openalex.org/C2987642246","wikidata":"https://www.wikidata.org/wiki/Q5452196","display_name":"First order","level":2,"score":0.3977999985218048},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.38929998874664307},{"id":"https://openalex.org/C39177556","wikidata":"https://www.wikidata.org/wiki/Q7100567","display_name":"Order of accuracy","level":4,"score":0.3828999996185303},{"id":"https://openalex.org/C165242687","wikidata":"https://www.wikidata.org/wiki/Q277932","display_name":"L-stability","level":5,"score":0.3822000026702881},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.3776000142097473},{"id":"https://openalex.org/C93226319","wikidata":"https://www.wikidata.org/wiki/Q193137","display_name":"Differential (mechanical device)","level":2,"score":0.3555000126361847},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.3434000015258789},{"id":"https://openalex.org/C500300565","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Computer simulation","level":2,"score":0.33550000190734863},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.33219999074935913},{"id":"https://openalex.org/C122700484","wikidata":"https://www.wikidata.org/wiki/Q16148845","display_name":"Exponential integrator","level":5,"score":0.2994999885559082},{"id":"https://openalex.org/C157977623","wikidata":"https://www.wikidata.org/wiki/Q2650267","display_name":"Predictor\u2013corrector method","level":2,"score":0.2935999929904938},{"id":"https://openalex.org/C147504518","wikidata":"https://www.wikidata.org/wiki/Q2146125","display_name":"Delay differential equation","level":3,"score":0.29269999265670776},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.28700000047683716},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2822999954223633},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.28209999203681946},{"id":"https://openalex.org/C122383733","wikidata":"https://www.wikidata.org/wiki/Q865920","display_name":"Approximation error","level":2,"score":0.28029999136924744},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.27459999918937683},{"id":"https://openalex.org/C97826883","wikidata":"https://www.wikidata.org/wiki/Q7069659","display_name":"Numerical partial differential equations","level":3,"score":0.260699987411499},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.25600001215934753}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.62762/jam.2026.326643","doi":"https://doi.org/10.62762/jam.2026.326643","is_oa":true,"landing_page_url":"https://doi.org/10.62762/jam.2026.326643","pdf_url":"https://www.icck.org/filebob/uploads/storage/JAM_uSKoruGy1SNCqriQk.pdf","source":{"id":"https://openalex.org/S5407049002","display_name":"ICCK Journal of Applied Mathematics","issn_l":"3068-5656","issn":["3068-5656"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICCK Journal of Applied Mathematics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.62762/jam.2026.326643","doi":"https://doi.org/10.62762/jam.2026.326643","is_oa":true,"landing_page_url":"https://doi.org/10.62762/jam.2026.326643","pdf_url":"https://www.icck.org/filebob/uploads/storage/JAM_uSKoruGy1SNCqriQk.pdf","source":{"id":"https://openalex.org/S5407049002","display_name":"ICCK Journal of Applied Mathematics","issn_l":"3068-5656","issn":["3068-5656"],"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"ICCK Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208815958.pdf","grobid_xml":"https://content.openalex.org/works/W7208815958.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133781348","https://openalex.org/W2060485879","https://openalex.org/W7124420487","https://openalex.org/W4411104056","https://openalex.org/W7166421748","https://openalex.org/W7168270304","https://openalex.org/W3216481437","https://openalex.org/W4390619972","https://openalex.org/W7220914810","https://openalex.org/W2022074290"],"abstract_inverted_index":{"This":[0],"paper":[1],"proposes":[2],"a":[3,29,133],"modified":[4],"two-point":[5],"block":[6],"backward":[7],"differentiation":[8],"formula":[9],"(MBBDF)":[10],"for":[11,60,143],"the":[12,43,52,61,87,91,96,105,109,144],"numerical":[13,62,137],"solution":[14,36,145],"of":[15,64,90,146],"highly":[16],"stiff":[17,65,83,147],"and":[18,33,74,76,98,116,125,140,148],"oscillatory":[19,149],"ordinary":[20,150],"differential":[21,151],"equations.":[22,152],"The":[23,69,127],"method":[24,70,112],"achieves":[25],"third-order":[26],"accuracy":[27,89,115],"with":[28],"reduced":[30],"error":[31],"constant":[32],"computes":[34],"two":[35],"values":[37],"simultaneously":[38],"at":[39],"each":[40],"step.":[41],"For":[42],"selected":[44],"parameter":[45],"value":[46,67],"$\\rho=-\\dfrac{7}{8}$,":[47],"stability":[48],"analysis":[49],"shows":[50],"that":[51,86,130],"resulting":[53],"scheme":[54],"is":[55,71],"A-stable,":[56],"making":[57],"it":[58],"suitable":[59],"integration":[63],"initial":[66],"problems.":[68],"also":[72],"consistent":[73],"zero-stable,":[75],"hence":[77],"convergent.":[78],"Numerical":[79],"experiments":[80],"on":[81,95],"benchmark":[82],"problems":[84],"show":[85],"relative":[88],"considered":[92],"methods":[93],"depends":[94],"problem":[97],"step":[99],"size.":[100],"While":[101],"2SBBDF":[102,124],"generally":[103],"produces":[104],"smallest":[106],"maximum":[107],"errors,":[108],"proposed":[110],"MBBDF":[111,131],"maintains":[113],"competitive":[114],"often":[117],"requires":[118],"substantially":[119],"less":[120],"computational":[121,141],"time":[122],"than":[123],"2ISBBDF.":[126],"results":[128],"indicate":[129],"provides":[132],"favorable":[134],"compromise":[135],"between":[136],"accuracy,":[138],"stability,":[139],"efficiency":[142]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-06T00:00:00"}