Asymptotic Methods for Systems of Differential Equations in which some Variables have very Short Response Times

Previous article Next article Asymptotic Methods for Systems of Differential Equations in which some Variables have very Short Response TimesD. B. MacMillanD. B. MacMillanhttps://doi.org/10.1137/0116058PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. J. Levin and , Norman Levinson, Singular perturbations of non-linear systems of differential equations and an associated boundary layer equation, J. Rational Mech. Anal., 3 (1954), 247–270 MR0061241 0055.08204 ISIGoogle Scholar[2] A. B. Vasil'eva, Asymptotic behaviour of solutions of certain problems for ordinary non-linear differential equations with a small parameter multiplying the highest derivatives, Russian Math. 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O’Malley, Jr.18 July 2006 | SIAM Review, Vol. 30, No. 2AbstractPDF (2159 KB)REFERENCES Cross Ref Solution algorithms for non-linear singularly perturbed optimal control problemsOptimal Control Applications and Methods, Vol. 4, No. 4 Cross Ref An Asymptotic Approximation for Singular PerturbationsW. F. Finden12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 43, No. 1AbstractPDF (1014 KB)Automatic Partitioning of Stiff Systems and Exploiting the Resulting StructureACM Transactions on Mathematical Software, Vol. 5, No. 4 Cross Ref Taylor series methods for the solution of the point reactor kinetics equationsAnnals of Nuclear Energy, Vol. 4, No. 4-5 Cross Ref The numerical solution of boundary value problems for stiff differential equations1 January 1977 | Mathematics of Computation, Vol. 31, No. 137 Cross Ref An effective numerical integration method for typical stiff systems17 June 2004 | AIChE Journal, Vol. 20, No. 2 Cross Ref An Upper Bound for the Singular Parameter in a Stable, Singularly Perturbed SystemJournal of the Franklin Institute, Vol. 295, No. 5 Cross Ref Stability, singular perturbations, and the vector Liénard equationIEEE Transactions on Automatic Control, Vol. 17, No. 4 Cross Ref Topics in singular perturbationsAdvances in Mathematics, Vol. 2, No. 4 Cross Ref Volume 16, Issue 4| 1968SIAM Journal on Applied Mathematics History Submitted:21 August 1967Published online:12 July 2006 InformationCopyright © 1968 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116058Article page range:pp. 704-722ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics