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.
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Cole J.D.: On a quasilinear parabolic equation occurring in aerodynamics. Q. Appl. Math. 9, 225–236 (1951)
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
Evans D.J., Abdullah A.R.: The group explicit method for the solution of Burgers equation. Computing 32, 239–253 (1984)
Hopf E.: The partial differential equation u t + uu x = ν u xx . Commun. Pure Appl. Math. 3, 201–230 (1950)
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)
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)
Pandey K., VermaL. Verma A.K.: On a finite difference scheme for Burgers equation. Appl. Math. Comput. 215, 2206–2214 (2009)
Smith G.D.: Numerical Solution of Partial Differential Equations. Oxford University Press, New York (1978)
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We are thankful to the reviewers for their expert comments and valuable suggestions.
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Pandey, K., Verma, L. & Verma, A.K. Du Fort–Frankel finite difference scheme for Burgers equation. Arab. J. Math. 2, 91–101 (2013). https://doi.org/10.1007/s40065-012-0050-1
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DOI: https://doi.org/10.1007/s40065-012-0050-1