Optical uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations
1996; Royal Society; Volume: 452; Issue: 1948 Linguagem: Inglês
10.1098/rspa.1996.0054
ISSN1471-2946
AutoresOvidiu Costin, Martin D. Kruskal,
Tópico(s)Advanced Numerical Analysis Techniques
ResumoRestricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Costin Ovidiu and Kruskal Martin David 1996Optical uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equationsProc. R. Soc. Lond. A.4521057–1085http://doi.org/10.1098/rspa.1996.0054SectionRestricted accessArticleOptical uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations Ovidiu Costin Google Scholar Find this author on PubMed Search for more papers by this author and Martin David Kruskal Google Scholar Find this author on PubMed Search for more papers by this author Ovidiu Costin Google Scholar Find this author on PubMed and Martin David Kruskal Google Scholar Find this author on PubMed Published:01 January 1996https://doi.org/10.1098/rspa.1996.0054AbstractFor first-order differential equations of the form y' = ∑pp(x)yp and second-order homogeneous linear differential equations y" + a(x)y' + b(x)y 0 with locally integrable coefficients having asymptotic (possibly divergent) power series when |x| —► oo on a ray arg(x) = const., under some further assumptions, it is shown that, on the given ray, there is a one-to-one correspondence between true solutions and (complete) formal solutions. The correspondence is based on asymptotic inequalities which are required to be uniform in x and optimal with respect to certain weights.FootnotesThis text was harvested from a scanned image of the original document using optical character recognition (OCR) software. As such, it may contain errors. Please contact the Royal Society if you find an error you would like to see corrected. Mathematical notations produced through Infty OCR. Previous ArticleNext Article VIEW FULL TEXT DOWNLOAD PDF FiguresRelatedReferencesDetailsCited by Dunne G and Ünsal M (2017) WKB and resurgence in the Mathieu equation Resurgence, Physics and Numbers, 10.1007/978-88-7642-613-1_6, (249-298), . Lastra A, Malek S and Sanz J (2015) Strongly Regular Multi-level Solutions of Singularly Perturbed Linear Partial Differential Equations, Results in Mathematics, 10.1007/s00025-015-0493-8, 70:3-4, (581-614), Online publication date: 1-Nov-2016. Boyd J (2014) The Fourier Transform of the quartic Gaussian exp(-Ax4): Hypergeometric functions, power series, steepest descent asymptotics and hyperasymptotics and extensions to exp(-Ax2n), Applied Mathematics and Computation, 10.1016/j.amc.2014.05.001, 241, (75-87), Online publication date: 1-Aug-2014. Lustri C and Chapman S (2013) Steady gravity waves due to a submerged source, Journal of Fluid Mechanics, 10.1017/jfm.2013.425, 732, (660-686), Online publication date: 10-Oct-2013. Garoufalidis S, Its A, Kapaev A and Mariño M (2011) Asymptotics of the Instantons of Painlevé I, International Mathematics Research Notices, 10.1093/imrn/rnr029, 2012:3, (561-606), ., Online publication date: 1-Jan-2012. Garoufalidis S and Mariño M (2010) Universality and asymptotics of graph counting problems in non-orientable surfaces, Journal of Combinatorial Theory, Series A, 10.1016/j.jcta.2009.10.013, 117:6, (715-740), Online publication date: 1-Aug-2010. Djakov P and Mityagin B (2005) Instability Zones of a Periodic 1D Dirac Operator and Smoothness of its Potential, Communications in Mathematical Physics, 10.1007/s00220-005-1347-0, 259:1, (139-183), Online publication date: 1-Oct-2005. Костин О, Costin O, Крускал М and Kruskal M (2002) Подвижные особые точки решений разностных уравнений, их связь с разрешимостью и исследование сверхстабильных фиксированных точекMovable Singularities of Solutions of Difference Equations in Relation to Solvability and a Study of a Superstable Fixed Point, Теоретическая и математическая физикаTeoreticheskaya i Matematicheskaya Fizika, 10.4213/tmf387, 133:2, (160-169), . Salvy B and Shackell J (1999) Symbolic Asymptotics: Multiseries of Inverse Functions, Journal of Symbolic Computation, 10.1006/jsco.1999.0281, 27:6, (543-563), Online publication date: 1-Jun-1999. Costin O On Borel summation and Stokes phenomena for rank-1 nonlinear systems of ordinary differential equations, Duke Mathematical Journal, 10.1215/S0012-7094-98-09311-5, 93:2 This Issue08 May 1996Volume 452Issue 1948 Article InformationDOI:https://doi.org/10.1098/rspa.1996.0054Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Manuscript received07/12/1994Manuscript accepted11/05/1995Published online01/01/1997Published in print01/01/1996 License:Scanned images copyright © 2017, Royal Society Citations and impact
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