๐”– Bobbio Scriptorium
โœฆ   LIBER   โœฆ

Give Your ODEs a Singular Perturbation!

โœ Scribed by Robert E. O'Malley Jr.

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
132 KB
Volume
251
Category
Article
ISSN
0022-247X

No coin nor oath required. For personal study only.

โœฆ Synopsis

Singular perturbations occur when, contrary to natural expectations, small changes produce substantial effects. Consequently, special methods to approximate solutions, both computational and otherwise, are needed. The topic can provide one way to increase interest, motivation, and applicability of an ODE course or follow-up studies. This presentation is aimed at those well-grounded in the traditional coverage of scalar first-order ordinary differential equations and series solutions, rather than an applied audience needing to learn singular perturbations per se to asymptotically solve some physical problem they face. After figuring out the impact of singular perturbations on these special equations, we encourage the consideration of analogous perturbations for more general ODEs or even PDEs.

๐Ÿ“œ SIMILAR VOLUMES

Singular Perturbation on a Subdomain
Singular Perturbation on a Subdomain
โœ G Aguilar; F Lisbona ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 229 KB

We consider a kind of singularly perturbed problem with a small positive parameter affecting the second order derivative only in a part of the domain. We analyse the existence and uniqueness of the solution and the asymptotic behaviour as the small parameter goes to zero.

Uniform convergence of a singular pertur
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โœ Luis A. Caffarelli; Antonio Cรณrdoba ๐Ÿ“‚ Article ๐Ÿ“… 2010 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 355 KB

where the interface bRl n R = bR2 n R is a "regular" surface with minimal area. This problem has been analyzed, among others, by De Giorgi, Franzone, and Ambrogio in [3] and[4], Can, Gurtin, and Slemrod in [2], Alikakos and Shaing in [l], Modica in [7], Modica and Mortola in [8], Kohn and Sternberg

A hyperbolic singular perturbation of Bu
A hyperbolic singular perturbation of Burgers' equation
โœ Benjamin F. Esham Jr. ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 524 KB

## Abstract This paper is concerned with the effect of perturbing Burgers' equation by a small term ฯต^2^ __U__~__tt__~. It is shown by means of an energy estimate that the solution of Burgers' equation provides a uniform __O__ (ฯต) approximation of the solution of the full hyperbolic problem. Existe