Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem
<p/> <p>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...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/102484 |
| Summary: | <p/> <p>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.</p> |
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| ISSN: | 1687-1839 1687-1847 |