Fitted finite difference method for singularly perturbed delay differential equations

Erdoğan F., Amiraliyev G. M.

NUMERICAL ALGORITHMS, cilt.59, sa.1, ss.131-145, 2012 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 59 Sayı: 1
  • Basım Tarihi: 2012
  • Doi Numarası: 10.1007/s11075-011-9480-7
  • Dergi Adı: NUMERICAL ALGORITHMS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.131-145
  • Van Yüzüncü Yıl Üniversitesi Adresli: Evet

Özet

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.

This paper deals with singularly perturbed initial value problem for linear second-order delay differential equation. An exponentially fitted difference scheme is constructed in an equidistant mesh, which gives first order uniform convergence in the discrete maximum norm. The difference scheme is shown to be uniformly convergent to the continuous solution with respect to the perturbation parameter. A numerical example is solved using the presented method and compared the computed result with exact solution of the problem.