Singular Perturbation Problems with a Singularity of the Second Kind.
Abstract
This paper deals with systems of singularly perturbed ordinary differential equations posed as boundary value problems on an infinite interval. The system is assumed to consist of singularly perturbed (fast) components and unperturbed (slow) components and to have a singularity of the second kind at infinity. Under the assumption that there is no turning point we derive uniform asymptotic expansions (as the perturbation parameter tends to zero) for the fast and slow components uniformly on the whole infinite line. The second goal of the paper is to derive convergence estimates for the solutions of 'finite' singular perturbation problems obtained by cutting the infinite interval at a finite (far out) point and by substituting appropriate additional boundary conditions at the far end. Using a suitable choice for these boundary conditions the order of convergence is shown to depend only on the decay property of the infinite solution.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1981
- Accession Number
- ADA110489
Entities
People
- Ch. A. Ringhofer
- Peter A. Markowich
Organizations
- University of Wisconsin–Madison