Numerical solution of a singularly perturbed three-point boundary value problem


Cakir M. , Amiraliyev G. M.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.84, ss.1465-1481, 2007 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 84 Konu: 10
  • Basım Tarihi: 2007
  • Doi Numarası: 10.1080/00207160701296462
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Sayfa Sayıları: ss.1465-1481

Özet

We consider a uniform finite difference method on an S-mesh (Shishkin type mesh) for a singularly perturbed semilinear one-dimensional convection-diffusion three-point boundary value problem with zeroth-order reduced equation. We show that the method is first-order convergent in the discrete maximum norm, independently of the perturbation parameter except for a logarithmic factor. An effective iterative algorithm for solving the non-linear difference problem and some numerical results are presented.