Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem

Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem

We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximu...

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Veröffentlicht in:Advances in difference equations 2010-01, Vol.2010 (1), p.102484-102484
1. Verfasser: Çakır, Musa
Format: Artikel
Sprache:eng
Schlagworte:
Algorithms
Boundary value problems
Mathematical models
Numerical analysis
Studies
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Zusammenfassung:We consider a singularly perturbed one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. The monotone operator is combined with the piecewise uniform Shishkin-type meshes. We show that the scheme is second-order convergent, in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. Numerical examples support the theoretical results.
ISSN:1687-1847
1687-1839
1687-1847
DOI:10.1186/1687-1847-2010-102484