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

Murat Sari*, Gürhan Gürarslan

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

71 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)475-483
Number of pages9
JournalApplied Mathematics and Computation
Volume208
Issue number2
DOIs
Publication statusPublished - 15 Feb 2009
Externally publishedYes

Keywords

  • Burgers' equation
  • Compact schemes
  • Finite difference method
  • Low-storage Runge-Kutta scheme

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