Naive singular perturbation theory

Mathematical Models and Methods in Applied Sciences

Volumn 11, Issue 1, 2001, Pages 119-131

  O'Malley Jr , Robert E ^a  

^a UNIVERSITY OF WASHINGTON   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0035583995     PISSN: 02182025     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218202501000787     Document Type: Article

References (22)

1. V. I. Arnold, V. V. Kozlov and A. I. Neishtadt, Mathematical Aspects of Classical and Celestial Mechanics (Springer, 1997).
2. E. Benoit, Dynamic Bifurcations, Lecture Notes in Math., Vol. 1493 (Springer-Verlag, 1991).
3. E. Benoit, A. Fruchard, R. Schäfke and G. Wallet, Overstability. Towards a global study, C. R. Acad. Sci. Paris 326 (1998) 873-878.
4. E. T. Copson, Asymptotic Expansions (Cambridge Univ. Press, 1965).
5. G. Dahlquist, On transformations of graded matrices with applications to stiff ODEs, Numer. Math. 47 (1985) 363-385.
6. G. Dahlquist, L. Edsberg, G. Skollermo and G. Soderlind, Are the numerical methods and software satisfactory for chemical kinetics?, in Lecture Notes in Math., Vol. 968 (Springer-Verlag, 1982), pp. 149-164.
7. Eds. F. Diener and M. Diener, Nonstandard Analysis in Practice (Springer, 1995).
8. R. Haberman, Slowly varying jump and transition phenomena associated with algebraic bifurcation problems, SIAM J. Appl. Math. 37 (1979) 69-106.
9. F. C. Hoppensteadt, Singular perturbations on the infinite interval, Trans. Amer. Math. Soc. 123 (1966) 521-535.
10. L. Kalachev and R. E. O'Malley, Jr., personal communication (1997).
11. J. Laforgue, "Exponential closeness to a repelling slow river and supersensitive shock or corner layers", talk at Luminy (1998).
12. J. J. Mahony and J. J. Shepherd, Stiff systems of ordinary differential equations II, J. Austral. Math. Soc. B23 (1981) 136-172.
13. N. N. Nefedov and K. R. Schneider, personal communication (1997).
14. A. I. Neishtadt (1987, 1988), Persistence of stability loss for dynamical bifurcations, Differential Equation 23 (1987) 2060-2067; 24 (1988) 171-176.
15. A. I. Neishtadt (1987, 1988), Persistence of stability loss for dynamical bifurcations, Differential Equation 23 (1987) 2060-2067; 24 (1988) 171-176.
16. Eds. J. A. Nohel and D. H. Sattinger, Selected Works of Norman Levinson, (Birkhäuser, 1998).
17. F. W. J. Olver, Asymptotics and Special Functions (Academic Press, 1974).
18. R. E. O'Malley, Jr., Singular Perturbation Methods for Ordinary Differential Equations (Springer-Verlag, 1991).
19. R. E. O'Malley, Jr., Stiff differential equations and singular perturbations, Research Report, Centre for Mathematics and its Applications, Australian National University (1996).
20. R. E. O'Malley, Jr., "Figuring out singular perturbations after a first course in ODEs", in Analyzing Multiscale Phenomena by Using Singular Perturbation Methods, eds. J. Cronin and R. E. O'Malley, Jr. (AMS, 1999), pp. 1-22.
21. M. A. Shishkova, Examination of a system of differential equations with a small parameter in the highest derivatives, Sov. Math. Dokl. 14 (1973) 483-487.
22. A. B. Vasil'eva, V. F. Butuzov and L. V. Kalachev, The Boundary Function Method for Singular Perturbations (SIAM, 1995).