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Singular Perturbations of Boundary Value Problems Involving Ordinary Differential Equations

Erdélyi, A. (1963) Singular Perturbations of Boundary Value Problems Involving Ordinary Differential Equations. Journal of the Society for Industrial and Applied Mathematics, 11 (1). pp. 105-116. ISSN 0368-4245. https://resolver.caltech.edu/CaltechAUTHORS:ERDjsiam63

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Abstract

In this lecture we shall consider boundary value problems Pε in which the order of the differential equation drops, or its type changes, as ε → 0 so that the boundary conditions prescribed in Pε are not appropriate when ε = 0, and it is not at all obvious how P0 should be defined. It is usually clear in such cases that limyε, if it exists, cannot satisfy all the limiting boundary conditions. In many cases limyε will not be attained uniformly, indeed limyε may be a discontinuous function; and the derivatives of yε may fail to approach a limit or may be unbounded functions of ε. A further characteristic feature of such "singular perturbation problems" is the nonanalytic dependence of yε on ε even in cases in which Pε depends on ε in a very simple manner. This nonanalytic dependence expresses itself frequently in a markedly different behaviour as ε approaches zero through positive or negative values.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1137/0111008DOIUNSPECIFIED
Additional Information:© 1963 Society for Industrial and Applied Mathematics. Received by the editors May 1, 1962. Invited address delivered at the meeting of SIAM in Pasadena, on March 24, 1962. The work was partly sponsored by the National Science Foundation under Grant No. G-19914.
Funders:
Funding AgencyGrant Number
National Science FoundationG-19914
Issue or Number:1
Record Number:CaltechAUTHORS:ERDjsiam63
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:ERDjsiam63
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:12096
Collection:CaltechAUTHORS
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Deposited On:22 Oct 2008 23:42
Last Modified:03 Oct 2019 00:25

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