{"id":"https://openalex.org/W2790401801","doi":"https://doi.org/10.1080/00207160.2018.1437263","title":"An explicit trigonometrically fitted Runge\u2013Kutta method for stiff and oscillatory problems with two frequencies","display_name":"An explicit trigonometrically fitted Runge\u2013Kutta method for stiff and oscillatory problems with two frequencies","publication_year":2018,"publication_date":"2018-02-07","ids":{"openalex":"https://openalex.org/W2790401801","doi":"https://doi.org/10.1080/00207160.2018.1437263","mag":"2790401801"},"language":"en","primary_location":{"id":"doi:10.1080/00207160.2018.1437263","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1437263","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","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/A5024286919","display_name":"Yonglei Fang","orcid":"https://orcid.org/0000-0002-5615-5971"},"institutions":[{"id":"https://openalex.org/I4210159676","display_name":"Zaozhuang University","ror":"https://ror.org/05x21tp94","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210159676"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yonglei Fang","raw_affiliation_strings":["Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-5615-5971","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, China","institution_ids":["https://openalex.org/I4210159676"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101804283","display_name":"Yang Yan-ping","orcid":"https://orcid.org/0000-0002-8245-334X"},"institutions":[{"id":"https://openalex.org/I4210159676","display_name":"Zaozhuang University","ror":"https://ror.org/05x21tp94","country_code":"CN","type":"education","lineage":["https://openalex.org/I4210159676"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yanping Yang","raw_affiliation_strings":["Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, China"],"raw_orcid":"https://orcid.org/0000-0002-8245-334X","affiliations":[{"raw_affiliation_string":"Department of Mathematics and Information Science, Zaozhuang University, Zaozhuang, China","institution_ids":["https://openalex.org/I4210159676"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004999123","display_name":"Xiong You","orcid":"https://orcid.org/0000-0002-0343-3878"},"institutions":[{"id":"https://openalex.org/I119454577","display_name":"Nanjing Agricultural University","ror":"https://ror.org/05td3s095","country_code":"CN","type":"education","lineage":["https://openalex.org/I119454577"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Xiong You","raw_affiliation_strings":["Colleges of Sciences, Nanjing Agricultural University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0002-0343-3878","affiliations":[{"raw_affiliation_string":"Colleges of Sciences, Nanjing Agricultural University, Nanjing, China","institution_ids":["https://openalex.org/I119454577"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5004999123"],"corresponding_institution_ids":["https://openalex.org/I119454577"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.04023448,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":98},"biblio":{"volume":"97","issue":"1-2","first_page":"85","last_page":"94"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11416","display_name":"Numerical methods for differential equations","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9991000294685364,"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/T11263","display_name":"Electromagnetic Simulation and Numerical Methods","score":0.9987000226974487,"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/runge\u2013kutta-methods","display_name":"Runge\u2013Kutta methods","score":0.8683842420578003},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.74836266040802},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.484309583902359},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4790269434452057},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.4511531591415405},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4063914120197296},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.15158158540725708}],"concepts":[{"id":"https://openalex.org/C181582579","wikidata":"https://www.wikidata.org/wiki/Q725944","display_name":"Runge\u2013Kutta methods","level":3,"score":0.8683842420578003},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.74836266040802},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.484309583902359},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4790269434452057},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.4511531591415405},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4063914120197296},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.15158158540725708},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/00207160.2018.1437263","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00207160.2018.1437263","pdf_url":null,"source":{"id":"https://openalex.org/S124867444","display_name":"International Journal of Computer Mathematics","issn_l":"0020-7160","issn":["0020-7160","1026-7425","1029-0265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Computer Mathematics","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1957402688","display_name":null,"funder_award_id":"11571302","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2046667580","display_name":null,"funder_award_id":"ZR2018AL05","funder_id":"https://openalex.org/F4320324174","funder_display_name":"Natural Science Foundation of Shandong Province"},{"id":"https://openalex.org/G2820032760","display_name":null,"funder_award_id":"BK20171370","funder_id":"https://openalex.org/F4320322769","funder_display_name":"Natural Science Foundation of Jiangsu Province"},{"id":"https://openalex.org/G7225647786","display_name":null,"funder_award_id":"J17KA190","funder_id":"https://openalex.org/F4320322522","funder_display_name":"Shandong University of Science and Technology"},{"id":"https://openalex.org/G8021993938","display_name":"\u57fa\u56e0\u8c03\u63a7\u7f51\u7edc\u632f\u5b50\u7684\u7ed3\u6784\u7406\u8bba\u4e0e\u4fdd\u7ed3\u6784\u6a21\u62df\u7814\u7a76","funder_award_id":"11171155","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"},{"id":"https://openalex.org/F4320322522","display_name":"Shandong University of Science and Technology","ror":"https://ror.org/04gtjhw98"},{"id":"https://openalex.org/F4320322769","display_name":"Natural Science Foundation of Jiangsu Province","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320324174","display_name":"Natural Science Foundation of Shandong Province","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W130160149","https://openalex.org/W1490397741","https://openalex.org/W1544770838","https://openalex.org/W1592347363","https://openalex.org/W1963830644","https://openalex.org/W1966978761","https://openalex.org/W1972279567","https://openalex.org/W1976493942","https://openalex.org/W1979657133","https://openalex.org/W1998819875","https://openalex.org/W2002066913","https://openalex.org/W2003266757","https://openalex.org/W2006038957","https://openalex.org/W2009437712","https://openalex.org/W2030376700","https://openalex.org/W2032954838","https://openalex.org/W2032971347","https://openalex.org/W2034182438","https://openalex.org/W2034818758","https://openalex.org/W2039943333","https://openalex.org/W2040679101","https://openalex.org/W2041123680","https://openalex.org/W2042388195","https://openalex.org/W2043091191","https://openalex.org/W2043322228","https://openalex.org/W2049431512","https://openalex.org/W2050874256","https://openalex.org/W2052243544","https://openalex.org/W2059632797","https://openalex.org/W2060423737","https://openalex.org/W2062666738","https://openalex.org/W2072364706","https://openalex.org/W2076112815","https://openalex.org/W2078427129","https://openalex.org/W2083763086","https://openalex.org/W2094679876","https://openalex.org/W2107379278","https://openalex.org/W2313019243","https://openalex.org/W2514372400","https://openalex.org/W2515448417","https://openalex.org/W2963170272","https://openalex.org/W2963842175"],"related_works":["https://openalex.org/W4206768127","https://openalex.org/W4213270568","https://openalex.org/W4244999877","https://openalex.org/W4301315183","https://openalex.org/W2083551655","https://openalex.org/W2069270950","https://openalex.org/W2082250026","https://openalex.org/W4224102766","https://openalex.org/W2474709654","https://openalex.org/W4285308861"],"abstract_inverted_index":{"In":[0],"this":[1],"paper,":[2],"a":[3],"new":[4,22,42,59],"explicit":[5],"fourth-order":[6],"Runge\u2013Kutta":[7],"method":[8,23,43,60],"adapted":[9],"to":[10,50],"oscillatory":[11],"problems":[12],"with":[13,63],"two":[14],"frequencies":[15],"(\u03bc":[16],"and":[17,32,37,55],"\u03bd)":[18],"is":[19],"developed.":[20],"The":[21],"can":[24],"integrate":[25],"exactly":[26],"the":[27,41,52,69],"different":[28],"harmonic":[29],"oscillators":[30],"y\u2032=i\u03bcy":[31],"y\u2032=i\u03bdy":[33],"simultaneously.":[34],"Numerical":[35,46],"stability":[36],"phase":[38],"properties":[39],"of":[40,57],"are":[44,48],"analysed.":[45],"experiments":[47],"conducted":[49],"illustrate":[51],"high":[53],"accuracy":[54],"competence":[56],"our":[58],"in":[61],"comparison":[62],"some":[64],"highly":[65],"effective":[66],"methods":[67],"from":[68],"recent":[70],"literature.":[71]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":5}],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}