{"id":"https://openalex.org/W2755560623","doi":"https://doi.org/10.1007/s11075-017-0408-8","title":"PDE-W-methods for parabolic problems with mixed derivatives","display_name":"PDE-W-methods for parabolic problems with mixed derivatives","publication_year":2017,"publication_date":"2017-09-09","ids":{"openalex":"https://openalex.org/W2755560623","doi":"https://doi.org/10.1007/s11075-017-0408-8","mag":"2755560623"},"language":"en","primary_location":{"id":"doi:10.1007/s11075-017-0408-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-017-0408-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","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/A5071096517","display_name":"S. Gonz\u00e1lez\u2010Pinto","orcid":"https://orcid.org/0000-0001-8714-862X"},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. Gonz\u00e1lez-Pinto","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain","institution_ids":["https://openalex.org/I158438070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026173495","display_name":"Ernst Hairer","orcid":"https://orcid.org/0000-0001-5057-2654"},"institutions":[{"id":"https://openalex.org/I114457229","display_name":"University of Geneva","ror":"https://ror.org/01swzsf04","country_code":"CH","type":"education","lineage":["https://openalex.org/I114457229"]}],"countries":["CH"],"is_corresponding":true,"raw_author_name":"E. Hairer","raw_affiliation_strings":["Section de math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, 1211, Geneva, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section de math\u00e9matiques, Universit\u00e9 de Gen\u00e8ve, 1211, Geneva, Switzerland","institution_ids":["https://openalex.org/I114457229"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025970096","display_name":"D. Hern\u00e1ndez\u2010Abreu","orcid":"https://orcid.org/0000-0003-1043-434X"},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"D. Hern\u00e1ndez-Abreu","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain","institution_ids":["https://openalex.org/I158438070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5025703808","display_name":"S. P\u00e9rez-Rodr\u00edguez","orcid":"https://orcid.org/0000-0002-3902-8313"},"institutions":[{"id":"https://openalex.org/I158438070","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25","country_code":"ES","type":"education","lineage":["https://openalex.org/I158438070"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"S. P\u00e9rez-Rodr\u00edguez","raw_affiliation_strings":["Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departamento de An\u00e1lisis Matem\u00e1tico, Universidad de La Laguna, 38071, La Laguna, Spain","institution_ids":["https://openalex.org/I158438070"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5026173495"],"corresponding_institution_ids":["https://openalex.org/I114457229"],"apc_list":{"value":2990,"currency":"USD","value_usd":2990},"apc_paid":null,"fwci":0.4189,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.58818306,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"78","issue":"3","first_page":"957","last_page":"981"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10339","display_name":"Advanced Numerical Methods in Computational Mathematics","score":0.9998000264167786,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.9997000098228455,"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/T11416","display_name":"Numerical methods for differential equations","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"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8283638954162598},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.7341619729995728},{"id":"https://openalex.org/keywords/theory-of-computation","display_name":"Theory of computation","score":0.6350283622741699},{"id":"https://openalex.org/keywords/numerical-analysis","display_name":"Numerical analysis","score":0.5937769412994385},{"id":"https://openalex.org/keywords/method-of-lines","display_name":"Method of lines","score":0.5417582988739014},{"id":"https://openalex.org/keywords/extension","display_name":"Extension (predicate logic)","score":0.524321436882019},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.5212222337722778},{"id":"https://openalex.org/keywords/alternating-direction-implicit-method","display_name":"Alternating direction implicit method","score":0.5174225568771362},{"id":"https://openalex.org/keywords/parabolic-partial-differential-equation","display_name":"Parabolic partial differential equation","score":0.4979076385498047},{"id":"https://openalex.org/keywords/partial-differential-equation","display_name":"Partial differential equation","score":0.4726088345050812},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4585305452346802},{"id":"https://openalex.org/keywords/numerical-methods-for-ordinary-differential-equations","display_name":"Numerical methods for ordinary differential equations","score":0.45247143507003784},{"id":"https://openalex.org/keywords/numerical-stability","display_name":"Numerical stability","score":0.44953423738479614},{"id":"https://openalex.org/keywords/linear-multistep-method","display_name":"Linear multistep method","score":0.4296822249889374},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4156704545021057},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.4120901823043823},{"id":"https://openalex.org/keywords/differential-equation","display_name":"Differential equation","score":0.33780765533447266},{"id":"https://openalex.org/keywords/finite-difference-method","display_name":"Finite difference method","score":0.22400987148284912},{"id":"https://openalex.org/keywords/ordinary-differential-equation","display_name":"Ordinary differential equation","score":0.2175869643688202},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.14626827836036682},{"id":"https://openalex.org/keywords/differential-algebraic-equation","display_name":"Differential algebraic equation","score":0.11962008476257324},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.11262238025665283},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.109129399061203}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8283638954162598},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.7341619729995728},{"id":"https://openalex.org/C24858836","wikidata":"https://www.wikidata.org/wiki/Q844718","display_name":"Theory of computation","level":2,"score":0.6350283622741699},{"id":"https://openalex.org/C48753275","wikidata":"https://www.wikidata.org/wiki/Q11216","display_name":"Numerical analysis","level":2,"score":0.5937769412994385},{"id":"https://openalex.org/C136798861","wikidata":"https://www.wikidata.org/wiki/Q1826712","display_name":"Method of lines","level":5,"score":0.5417582988739014},{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.524321436882019},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.5212222337722778},{"id":"https://openalex.org/C142363948","wikidata":"https://www.wikidata.org/wiki/Q4736413","display_name":"Alternating direction implicit method","level":3,"score":0.5174225568771362},{"id":"https://openalex.org/C186867907","wikidata":"https://www.wikidata.org/wiki/Q1575416","display_name":"Parabolic partial differential equation","level":3,"score":0.4979076385498047},{"id":"https://openalex.org/C93779851","wikidata":"https://www.wikidata.org/wiki/Q271977","display_name":"Partial differential equation","level":2,"score":0.4726088345050812},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4585305452346802},{"id":"https://openalex.org/C1164432","wikidata":"https://www.wikidata.org/wiki/Q541182","display_name":"Numerical methods for ordinary differential equations","level":5,"score":0.45247143507003784},{"id":"https://openalex.org/C176321772","wikidata":"https://www.wikidata.org/wiki/Q1430640","display_name":"Numerical stability","level":3,"score":0.44953423738479614},{"id":"https://openalex.org/C65889100","wikidata":"https://www.wikidata.org/wiki/Q1462003","display_name":"Linear multistep method","level":5,"score":0.4296822249889374},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4156704545021057},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.4120901823043823},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.33780765533447266},{"id":"https://openalex.org/C205951836","wikidata":"https://www.wikidata.org/wiki/Q1147751","display_name":"Finite difference method","level":2,"score":0.22400987148284912},{"id":"https://openalex.org/C51544822","wikidata":"https://www.wikidata.org/wiki/Q465274","display_name":"Ordinary differential equation","level":3,"score":0.2175869643688202},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.14626827836036682},{"id":"https://openalex.org/C186219872","wikidata":"https://www.wikidata.org/wiki/Q955889","display_name":"Differential algebraic equation","level":4,"score":0.11962008476257324},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.11262238025665283},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.109129399061203},{"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/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1007/s11075-017-0408-8","is_oa":false,"landing_page_url":"https://doi.org/10.1007/s11075-017-0408-8","pdf_url":null,"source":{"id":"https://openalex.org/S117494069","display_name":"Numerical Algorithms","issn_l":"1017-1398","issn":["1017-1398","1572-9265"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Numerical Algorithms","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Zero hunger","score":0.5199999809265137,"id":"https://metadata.un.org/sdg/2"}],"awards":[],"funders":[{"id":"https://openalex.org/F4320315877","display_name":"Universidad de La Laguna","ror":"https://ror.org/01r9z8p25"},{"id":"https://openalex.org/F4320323830","display_name":"Universit\u00e9 de Gen\u00e8ve","ror":"https://ror.org/01swzsf04"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1509923322","https://openalex.org/W1594880188","https://openalex.org/W1902819800","https://openalex.org/W2003372231","https://openalex.org/W2010210658","https://openalex.org/W2047725321","https://openalex.org/W2051559783","https://openalex.org/W2092439997","https://openalex.org/W2095036901","https://openalex.org/W2114084519","https://openalex.org/W2117842679","https://openalex.org/W2126408836","https://openalex.org/W2160470702","https://openalex.org/W2162277293","https://openalex.org/W2184962859","https://openalex.org/W2186711713","https://openalex.org/W2191169687","https://openalex.org/W2203953893","https://openalex.org/W2526347135","https://openalex.org/W2582972221"],"related_works":["https://openalex.org/W2769508618","https://openalex.org/W2023917379","https://openalex.org/W2065798545","https://openalex.org/W2002986295","https://openalex.org/W4210888083","https://openalex.org/W1970784083","https://openalex.org/W1983404831","https://openalex.org/W1977572928","https://openalex.org/W4245390618","https://openalex.org/W1984325333"],"abstract_inverted_index":null,"counts_by_year":[{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":6},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1}],"updated_date":"2026-07-29T09:40:50.615796","created_date":"2025-10-10T00:00:00"}