Abstract
The singular perturbation boundary-value problem exhibits anomalous behavior in its first integral equation, while the numerical solution behaves reasonably. Numerical study of the first integral equation defines conditions under which the anomalous behavior occurs.
Similar content being viewed by others
References
Howes, F. A.,Some Old and New Results on Singularly Perturbed Boundary-Value Problems, Singular Perturbations and Asymptotics, Edited by R. E. Meyer and S. V. Parter, Academic Press, New York, New York, pp. 41–86, 1980.
Abramowitz, M., andStegun, I. A.,Handbook of Mathematical Functions, Chapter 17, Elliptic Integrals, Dover Publications, New York, New York, 1965.
Byrd, P. F., andFriedman, M. D.,Handbook of Elliptic Integrals for Engineers and Physicists, Springer-Verlag, Berlin, Germany, 1954.
Dahlquist, G., andBjorck, A.,Numerical Methods, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 290–293, 1974.
Gear, G. W.,Numerical Initial-Value Problems in Ordinary Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, pp. 96–99, 1971.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Roberts, S.M. On the solution of εy″=y 3 . J Optim Theory Appl 50, 535–541 (1986). https://doi.org/10.1007/BF00938636
Issue Date:
DOI: https://doi.org/10.1007/BF00938636