Optimal uniform estimates and rigorous asymptotics beyond all orders for a class of ordinary differential equations

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 452, Issue 1948, 1996, Pages 1057-1085

  Costin, Ovidiu ^a   Kruskal, Martin D ^b  

^a UNIVERSITY OF CHICAGO   (United States)

^b RUTGERS UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746710071     PISSN: 13645021     EISSN: None     Source Type: Journal    
DOI: 10.1098/rspa.1996.0054     Document Type: Article

References (17)

1. Berry, M. V. 1989 Uniform asymptotic smoothing of Stokes' discontinuities. Proc. R. Soc. Land. A 422, 7-21.
2. Berry, M. V. 1990 Waves near Stokes lines. Proc. R. Soc. Land. A 427, 265-280.
3. Coddington, E. & Levinson, N. 1955 Theory of ordinary differential equations. New York: McGraw-Hill.
4. Cope, F. T. 1934 Formal solutions of irregular differential equations. Part I. Am. J. Math. 56, 411-437.
5. Dingle, R. B. 1973 Asymptotic expansions: their derivation and interpretation. Academic Press.
6. Ecalle, J. 1981 Fonctions résurgentes. Publications Mathématiques D'Orsay.
7. Ecalle, J. 1990 Finitude des cycles limites et accelero-sommation de l'application de retour. Université de Paris-Sud Preprint 90-36.
8. Ecalle, J. 1993 Transseries, analysable functions and Dulac's conjecture. In Bifurcations and periodic orbits of vector fields (ed. D. Schlomiuk). NATO ASI Series C, vol. 408. Kluwer.
9. Jurkat, W., Lutz, D. & Peyerimhoff, A. 1976 Birkhoff invariants and effective calculations for meromorphic linear differential equations. J. Math. Analysis Applicat. 53, 438-470.
10. Kruskal, M. D. & Segur, H. 1991 Asymptotics beyond all orders in a model of crystal growth. Stud. Appl. Math. 85, 129-181.
11. McLeod, J. B. 1992 Smoothing of Stokes discontinuities. Proc. R. Soc. Land. A 437, 343-354.
12. Ramis, J. P. 1978 Devissage Gevrey. Astérisque 59-60, 173-204.
13. Ritt, J. F. 1950 Differential algebra. New York: American Mathematical Society.
14. Segur, H., Tanveer, S. & Levine, H. (eds) 1991 Asymptotics beyond all orders. Plenum Press.
15. Sibuya, Y. 1975 Global theory of a second order linear ordinary differential equation with a polynomial coefficient. North-Holland.
16. Stokes, G. G. 1857 Trans. Camb. Phil. Soc. 10, 106-128. Reprinted in Mathematical and physical papers by late Sir George Gabriel Stokes, vol. IV, 77-109 (1904). Cambridge University Press.
17. Wasow, W. 1968 Asymptotic expansions for ordinary differential equations. Interscience Publishers.