{"id":"https://openalex.org/W2995503881","doi":"https://doi.org/10.1142/s1793962320500014","title":"Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation","display_name":"Variable-step-size second-order-derivative multistep method for solving first-order ordinary differential equations in system simulation","publication_year":2019,"publication_date":"2019-12-16","ids":{"openalex":"https://openalex.org/W2995503881","doi":"https://doi.org/10.1142/s1793962320500014","mag":"2995503881"},"language":"en","primary_location":{"id":"doi:10.1142/s1793962320500014","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320500014","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and 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/A5100637601","display_name":"Lei Zhang","orcid":"https://orcid.org/0000-0002-8481-5914"},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lei Zhang","raw_affiliation_strings":["School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China","institution_ids":["https://openalex.org/I173899330"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Chaofeng Zhang","orcid":"https://orcid.org/0000-0003-3118-8117"},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chaofeng Zhang","raw_affiliation_strings":["School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China"],"raw_orcid":"https://orcid.org/0000-0003-3118-8117","affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China","institution_ids":["https://openalex.org/I173899330"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101839723","display_name":"Mengya Liu","orcid":"https://orcid.org/0000-0003-4367-4542"},"institutions":[{"id":"https://openalex.org/I173899330","display_name":"Henan University","ror":"https://ror.org/003xyzq10","country_code":"CN","type":"education","lineage":["https://openalex.org/I173899330"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Mengya Liu","raw_affiliation_strings":["School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Physics and Electronics, Henan University, Kaifeng, Henan 475004, P. R. China","institution_ids":["https://openalex.org/I173899330"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I173899330"],"apc_list":null,"apc_paid":null,"fwci":0.3246,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.58409926,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"11","issue":"01","first_page":"2050001","last_page":"2050001"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9994999766349792,"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 methods for 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/T12810","display_name":"Real-time simulation and control systems","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9940000176429749,"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/linear-multistep-method","display_name":"Linear multistep method","score":0.7662239074707031},{"id":"https://openalex.org/keywords/truncation-error","display_name":"Truncation error","score":0.7371488809585571},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6897380352020264},{"id":"https://openalex.org/keywords/variable","display_name":"Variable (mathematics)","score":0.6669585108757019},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5937818288803101},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5890846848487854},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.5847878456115723},{"id":"https://openalex.org/keywords/backward-differentiation-formula","display_name":"Backward differentiation formula","score":0.5626587867736816},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.5433377623558044},{"id":"https://openalex.org/keywords/hermite-interpolation","display_name":"Hermite interpolation","score":0.5178151726722717},{"id":"https://openalex.org/keywords/derivative","display_name":"Derivative (finance)","score":0.48702317476272583},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.4823743402957916},{"id":"https://openalex.org/keywords/hermite-polynomials","display_name":"Hermite polynomials","score":0.4745505750179291},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.4557506740093231},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.44782203435897827},{"id":"https://openalex.org/keywords/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.4388641119003296},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.3440561592578888},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.2320258915424347},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.16546311974525452}],"concepts":[{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.7662239074707031},{"id":"https://openalex.org/C104942944","wikidata":"https://www.wikidata.org/wiki/Q3434686","display_name":"Truncation error","level":2,"score":0.7371488809585571},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6897380352020264},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.6669585108757019},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5937818288803101},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5890846848487854},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.5847878456115723},{"id":"https://openalex.org/C152522140","wikidata":"https://www.wikidata.org/wiki/Q795746","display_name":"Backward differentiation formula","level":5,"score":0.5626587867736816},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.5433377623558044},{"id":"https://openalex.org/C186429297","wikidata":"https://www.wikidata.org/wiki/Q44451","display_name":"Hermite interpolation","level":3,"score":0.5178151726722717},{"id":"https://openalex.org/C111771559","wikidata":"https://www.wikidata.org/wiki/Q66295","display_name":"Derivative (finance)","level":2,"score":0.48702317476272583},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.4823743402957916},{"id":"https://openalex.org/C201362023","wikidata":"https://www.wikidata.org/wiki/Q658574","display_name":"Hermite polynomials","level":2,"score":0.4745505750179291},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.4557506740093231},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.44782203435897827},{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.4388641119003296},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.3440561592578888},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.2320258915424347},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.16546311974525452},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C106159729","wikidata":"https://www.wikidata.org/wiki/Q2294553","display_name":"Financial economics","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s1793962320500014","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s1793962320500014","pdf_url":null,"source":{"id":"https://openalex.org/S107361000","display_name":"Advances in Complex Systems","issn_l":"0219-5259","issn":["0219-5259","1793-6802","1793-9615","1793-9623"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Modeling, Simulation, and Scientific Computing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3774283542","display_name":null,"funder_award_id":"61773008","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":15,"referenced_works":["https://openalex.org/W1654509461","https://openalex.org/W1968512837","https://openalex.org/W1989621225","https://openalex.org/W1990421076","https://openalex.org/W1993964995","https://openalex.org/W1997933267","https://openalex.org/W2020344169","https://openalex.org/W2054024140","https://openalex.org/W2057998877","https://openalex.org/W2076047216","https://openalex.org/W2077810706","https://openalex.org/W2291829050","https://openalex.org/W2528472629","https://openalex.org/W2577664770","https://openalex.org/W2604260862"],"related_works":["https://openalex.org/W2054077382","https://openalex.org/W832825236","https://openalex.org/W2052381424","https://openalex.org/W2065445194","https://openalex.org/W2378531610","https://openalex.org/W1579385565","https://openalex.org/W2044386336","https://openalex.org/W4317934108","https://openalex.org/W2136451125","https://openalex.org/W2361181988"],"abstract_inverted_index":{"According":[0],"to":[1,52],"the":[2,37,42,60,68],"relationship":[3],"between":[4],"truncation":[5],"error":[6],"and":[7,23,41,73],"step":[8],"size":[9],"of":[10,36,70],"two":[11],"implicit":[12],"second-order-derivative":[13],"multistep":[14],"formulas":[15,38],"based":[16],"on":[17],"Hermite":[18],"interpolation":[19],"polynomial,":[20],"a":[21,53],"variable-order":[22],"variable-step-size":[24],"numerical":[25,61],"method":[26,62],"for":[27],"solving":[28],"differential":[29],"equations":[30],"is":[31],"designed.":[32],"The":[33,47,56],"stability":[34,43],"properties":[35],"are":[39,45,50],"discussed":[40],"regions":[44],"analyzed.":[46],"deduced":[48],"methods":[49],"applied":[51],"simulation":[54],"problem.":[55],"results":[57],"show":[58],"that":[59],"can":[63],"satisfy":[64],"calculation":[65,71,75],"accuracy,":[66],"reduce":[67],"number":[69],"steps":[72],"accelerate":[74],"speed.":[76]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2026-06-26T08:34:08.712188","created_date":"2025-10-10T00:00:00"}