Singular Perturbation Problems with a Singularity of the Second Kind.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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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.
- Numerical Mathematics