## Robust a posteriori error bounds for spline collocation applied to singularly perturbed reaction-diffusion problems

### Abstract

Collocation with arbitrary order $C^1$-splines for a singularly perturbed reaction-diffusion problem in one dimension is studied. Robust a posteriori error bounds are derived for the collocation method on arbitrary meshes. These bounds are used to drive an adaptive mesh moving algorithm. Numerical results are presented.

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### Key words

reaction-diffusion, spline collocation, singular perturbations, a posteriori error estimation

### AMS subject classifications

65L10, 65L11, 65L60

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