Numerical treatment of a quasilinear initial value problem with boundary layer


Çakır M., Çimen E., Amirali I., Amiraliyev G.

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS, cilt.93, ss.1845-1859, 2016 (SCI İndekslerine Giren Dergi)

  • Cilt numarası: 93 Konu: 11
  • Basım Tarihi: 2016
  • Doi Numarası: 10.1080/00207160.2015.1076805
  • Dergi Adı: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS
  • Sayfa Sayısı: ss.1845-1859

Özet

The paper deals with the singularly perturbed quasilinear initial value problem exhibiting initial layer. First the nature of solution of differential problem before presenting method for its numerical solution is discussed. The numerical solution of the problem is performed with the use of a finite-fitted difference scheme on an appropriate piecewise uniform mesh (Shishkin-type mesh). An error analysis shows that the method is first-order convergent except for a logarithmic factor, in the discrete maximum norm, independently of the perturbation parameter. Finally, numerical results supporting the theory are presented.