Uniform Second-Order Difference Method for a Singularly Perturbed Three-Point Boundary Value Problem - Çakır Musa (Advances in Difference Equations, 2010)
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.