Arabian Journal of Mathematics

, Volume 2, Issue 1, pp 91–101 | Cite as

Du Fort–Frankel finite difference scheme for Burgers equation

Open Access
Research Article

Abstract

In this paper we apply the Du Fort–Frankel finite difference scheme on Burgers equation and solve three test problems. We calculate the numerical solutions using Mathematica 7.0 for different values of viscosity. We have considered smallest value of viscosity as 10−4 and observe that the numerical solutions are in good agreement with the exact solution.

Mathematics Subject Classification

65N06 

References

  1. 1.
    Cole J.D.: On a quasilinear parabolic equation occurring in aerodynamics. Q. Appl. Math. 9, 225–236 (1951)MATHGoogle Scholar
  2. 2.
    Dhawan, S.; Kapoor, S.; Kumar, S.; Rawat, S.: Contemporary review of techniques for the solution of nonlinear Burgers equation. J. Comput. Sci. doi:10.1016/j.jocs.2012.06.003
  3. 3.
    Evans D.J., Abdullah A.R.: The group explicit method for the solution of Burgers equation. Computing 32, 239–253 (1984)MATHMathSciNetCrossRefGoogle Scholar
  4. 4.
    Hopf E.: The partial differential equation ut + uux = ν uxx. Commun. Pure Appl. Math. 3, 201–230 (1950)MATHMathSciNetCrossRefGoogle Scholar
  5. 5.
    Kutluay S., Bahadir A.R., Ozdes A.: Numerical solution of one-dimensional Burgers equation: explicit and exact explicit methods. J. Comput. Appl. Math. 103, 251–261 (1999)MATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Mittal, R.C.; Jain, R.K.: Numerical solutions of nonlinear Burgers equation with modified cubic B-splines collocation method. Appl. Math. Comput. 218(15), 7839–7855 (2012)Google Scholar
  7. 7.
    Pandey K., VermaL. Verma A.K.: On a finite difference scheme for Burgers equation. Appl. Math. Comput. 215, 2206–2214 (2009)MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Smith G.D.: Numerical Solution of Partial Differential Equations. Oxford University Press, New York (1978)MATHGoogle Scholar

Copyright information

© The Author(s) 2012

This article is published under license to BioMed Central Ltd. Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.

Authors and Affiliations

  1. 1.Department of Mathematics and AstronomyUniversity of LucknowLucknowIndia
  2. 2.Department of MathematicsBITS PilaniPilaniIndia

Personalised recommendations