Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Cash J. R. 2003Review Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equationsProc. R. Soc. Lond. A.459797–815http://doi.org/10.1098/rspa.2003.1130SectionRestricted accessReview Paper: Efficient numerical methods for the solution of stiff initial-value problems and differential algebraic equations J. R. Cash J. R. Cash Department of Mathematics, Imperial College of Science, Technology and Medicine, South Kensington, London SW7 2AZ, UK Google Scholar Find this author on PubMed Search for more papers by this author J. R. Cash J. R. Cash Department of Mathematics, Imperial College of Science, Technology and Medicine, South Kensington, London SW7 2AZ, UK Google Scholar Find this author on PubMed Search for more papers by this author Published:08 April 2003https://doi.org/10.1098/rspa.2003.1130AbstractIn recent years, after a prolonged period of intense activity, the study of numerical methods for solving stiff initial-value problems for ordinary differential equations and differential algebraic equations has reached a certain maturity. There now exist some excellent codes which are both efficient and reliable for solving these particular classes of problems. In this paper, we sketch some of the main theory which underpins stiff integration methods and we use this to describe, and put into context, some of the best codes currently available. By referencing only codes which have been thoroughly tested and are widely available, our aim is to direct users of numerical software to those codes which they should try initially if faced with the problem of solving ordinary differential equations of this type. An additional feature is that the codes which we propose serve as benchmarks against which any new codes can be evaluated. Next Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Wen C, Meng X, Xie Y, Liu R, Kong X, Li R, Liu Z and Fang C (2021) Online measurement of piston-assembly friction with wireless IMEP method under fired conditions and comparison with numerical analysis, Measurement, 10.1016/j.measurement.2021.109009, 174, (109009), Online publication date: 1-Apr-2021. D’Ambrosio R and Paternoster B (2021) Multivalue collocation methods free from order reduction, Journal of Computational and Applied Mathematics, 10.1016/j.cam.2019.112515, 387, (112515), Online publication date: 1-May-2021. 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