Abstract
The problem of constructing a parameter-uniform numerical method for a singularly perturbed self-adjoint ordinary differential equation is considered. It is shown that a suitably designed discrete Schwarz method, based on a standard finite difference operator with a uniform mesh on each subdomain, gives numerical approximations which converge in the maximum norm to the exact solution, uniformly with respect to the singular perturbation parameter. This parameter-uniform convergence is shown to be essentially second order. That this new discrete Schwarz method is efficient in practice is demonstrated by numerical experiments.
Original language | English |
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Pages (from-to) | 231-244 |
Number of pages | 14 |
Journal | Journal of Computational and Applied Mathematics |
Volume | 130 |
Issue number | 1-2 |
DOIs | |
Publication status | Published - 1 May 2001 |
Externally published | Yes |
Keywords
- Parameter-uniform
- Reaction-diffusion
- Schwarz
- Singularly perturbed