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

Cakir M.

ADVANCES IN DIFFERENCE EQUATIONS, 2010 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası:
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1155/2010/102484
  • Dergi Adı: ADVANCES IN DIFFERENCE EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

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.