A Numerical Study on the Difference Solution of Singularly Perturbed Semilinear Problem with Integral Boundary Condition


Çakır M.

MATHEMATICAL MODELLING AND ANALYSIS, cilt.21, ss.644-658, 2016 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 21 Konu: 5
  • Basım Tarihi: 2016
  • Doi Numarası: 10.3846/13926292.2016.1201702
  • Dergi Adı: MATHEMATICAL MODELLING AND ANALYSIS
  • Sayfa Sayıları: ss.644-658

Özet

The present study is concerned with the numerical solution, using finite difference method on a piecewise uniform mesh (Shishkin type mesh) for a singularly perturbed semilinear boundary value problem with integral boundary condition. First we discuss the nature of the continuous solution of singularly perturbed differential problem before presenting method for its numerical solution. The numerical method is constructed on piecewise uniform Shishkin type mesh. We show that the method is first-order convergent in the discrete maximum norm, independently of singular perturbation parameter except for a logarithmic factor. We give effective iterative algorithm for solving the nonlinear difference problem. Numerical results which support the given estimates are presented.