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The θ-method is applied to solve approximately the system of ODEs on a set of prescribed grid-points. If N is the number of time-steps that are to be carried out, then this numerical method can be defined by using the following set of relationships y n ∈=∈y n∈-∈1∈+∈h (1∈-∈θ) f(t n∈-∈1, y n∈-∈1) , θ∈ ∈[0.5, 1.0] , n∈=∈1, 2, ..., N , h∈=∈(b∈-∈a) / N , t n ∈=∈t n∈-∈1∈+∈h∈=∈t 0∈+∈ n h , t 0=∈a , t N =∈b . As a rule, the accuracy of the approximations { y n | n∈=∈1, 2, ..., N } , can be improved by applying the Richardson Extrapolation under the assumption that the stability of the computational process is preserved. Therefore, it is natural to require that the combined numerical method (Richardson Extrapolation plus the θ-method) is in some sense stable. It can be proved that the combined method is strongly A-stable when θ∈ ∈[2/3, 1.0] . This is the main result in the paper. The usefulness of this result in the solution of many problems arising in different scientific and engineering areas is demonstrated by performing a series of experiments with an extremely badly-scaled and very stiff atmospheric chemistry scheme which is actually used in several well-known large-scale air pollution models. © 2010 Springer-Verlag Berlin Heidelberg.", "digital" : null, "printed" : null, "sourceYear" : 2012, "packet" : "(Havasi Ágnes (Meteorológia); 2011.11.10. 19:17:01)", "foreignEdition" : true, "foreignLanguage" : true, "fullPublication" : false, "conferencePublication" : true, "nationalOrigin" : null, "missingAuthor" : false, "oaType" : "PAY", "oaCheckDate" : "2024-03-25", "oaFree" : false, "citationCount" : 0, "citationCountUnpublished" : 0, "citationCountWoOther" : 0, "independentCitCountWoOther" : 0, "nationalOriginCitationCount" : 0, "foreignEditionCitationCount" : 0, "doiCitationCount" : 0, "wosCitationCount" : 0, "scopusCitationCount" : 0, "wosScopusCitationCount" : 0, "wosScopusCitationCountWoOther" : 0, "wosScopusIndependentCitationCount" : 0, "wosScopusIndependentCitationCountWoOther" : 0, "independentCitationCount" : 0, "selfCitationCount" : 0, "unhandledCitationCount" : 0, "citingPubCount" : 0, "independentCitingPubCount" : 0, "citingPubCountWoOther" : 0, "independentCitingPubCountWoOther" : 0, "unhandledCitingPubCount" : 0, "citedPubCount" : 0, "citedCount" : 0, "references" : [ { "otype" : "Reference", "mtid" : 1430105, "link" : "/api/reference/1430105", "label" : "1. 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