A sixth-order compact finite difference scheme to the numerical solutions of Burgers' equation

SARI M., Gurarslan G.

APPLIED MATHEMATICS AND COMPUTATION, cilt.208, sa.2, ss.475-483, 2009 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 208 Sayı: 2
  • Basım Tarihi: 2009
  • Doi Numarası: 10.1016/j.amc.2008.12.012
  • Dergi Adı: APPLIED MATHEMATICS AND COMPUTATION
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.475-483
  • Yıldız Teknik Üniversitesi Adresli: Hayır

Özet

A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge-Kutta scheme in time have been combined. The scheme is implemented to solve two test problems with known exact solutions. Comparisons of the computed results with exact solutions showed that the method is capable of achieving high accuracy and efficiency with minimal computational effort. The present results are also seen to be more accurate than some available results given in the literature. (C) 2008 Elsevier Inc. All rights reserved.