Die gleichmäßige Stabilität singulär gestörter diskreter und kontinuierlicher Randwertprobleme
- Cite this article as:
- Niederdrenk, K. & Yserentant, H. Numer. Math. (1983) 41: 223. doi:10.1007/BF01390214
The uniform stability of singularly perturbed discrete and continuous boundary value problems
In this paper we consider singular perturbation problems for ordinary differential operators of ordern and their discrete counterparts on arbitrary nonuniform grids. We prove that the singularly perturbed initial value problem is stable uniformly in the perturbation parameter ε in both the continuous and the discrete case. We use this result to characterize the stability of the corresponding continuous and discrete boundary value problems. If the continuous problem is stable and if the consistency error is smaller than a certain constant, the discrete problem is also stable.