424
Views
14
CrossRef citations to date
0
Altmetric
Section B

Efficient and accurate finite difference schemes for solving one-dimensional Burgers’ equation

&
Pages 2575-2590 | Received 27 Jun 2010, Accepted 02 Dec 2010, Published online: 25 May 2011

References

  • Aksan , E. N. and Ozdes , A. 2004 . A numerical solution of Burgers's equation . Appl. Math. Comput. , 156 : 395 – 402 .
  • Bateman , H. 1915 . Some recent researches on the motion of fluids . Mon. Weather Rev. , 43 : 163 – 170 .
  • Bringen , S. and Saati , A. 1990 . Comparison of several finite-difference methods . J. Aircraft , 27 : 90 – 99 .
  • Burg , C. and Erwin , T. 2009 . Application of Richardson extrapolation to the numerical solution of partial differential equations . Numer. Meth. Partial Differential Equations , 25 ( 4 ) : 810 – 832 .
  • Burger , J. M. 1948 . A Mathematical Model Illustrating the Theory of Turbulence , 171 – 199 . New York : Academic Press . Advances in Applied Mechanics, vol. I
  • Caldwell , J. and Smith , P. 1982 . Solution of Burgers’ equation with a large Reynolds number . Appl. Math. Model. , 6 : 381 – 385 .
  • Cole , J. D. 1951 . On a quasilinear parabolic equations occurring in aerodynamics . Quart. Appl. Math. , 9 : 225 – 236 .
  • Evans , D. J. and Abdullah , A. R. 1984 . The group explicit method for the solution of Burgers’ equation . Quart. Appl. Math. , 30 : 239 – 253 .
  • Hassanien , I. A. , Salama , A. A. and Hosham , H. A. 2005 . Fourth-order finite difference method for solving Burgers’ equation . Appl. Math. Comput. , 170 : 781 – 800 .
  • Hon , Y. C. and Mao , X. Z. 1998 . An efficient numerical scheme for Burgers’ equation . Appl. Math. Comput. , 95 : 37 – 50 .
  • Hopf , E. 1950 . The partial differential equation . Commun. Pure Appl. Math. , 3 : 201 – 230 .
  • Huang , P. and Abduwali , A. 2010 . The modified local Crank–Nicolson method for one- and two-dimensional Burgers’ equations . Comput. Math. Appl , 59 ( 8 ) : 2452 – 2463 .
  • Hundsdorfer , W. and Verwer , J. G. 2003 . Numerical Solution of Time-dependent Advection–Diffusion–Reaction Equations , Berlin : Springer .
  • Kadalbajoo , M. K. and Awasthi , A. 2006 . A numerical method based on Crank–Nicholson scheme for Burgers’ equation . Appl. Math. Comput. , 182 : 1430 – 1442 .
  • Kutluay , S. , Bahadir , A. R. and Ozdes , A. 1999 . Numerical solution of one-dimensional Burgers equation: Explicit and exact-explicit finite difference methods . J. Comput. Appl. Math. , 103 : 251 – 261 .
  • Liao , W. 2008 . An implicit fourth-order compact finite difference scheme for one-dimensional Burgers’ equation . Appl. Math. Comput , 206 ( 2 ) : 755 – 764 .
  • Liao , W. , Zhu , J. and Khaliq , A. Q.M. 2006 . A fourth-order compact algorithm for nonlinear Reaction-Diffusion equations with Neumann boundary conditions . Numer. Meth. Partial Differential Equations , 22 : 600 – 616 .
  • Ozis , T. and Aslan , Y. 2005 . The semi-approximate approach for solving Burgers’ equation with high Reynolds number . Appl. Math. Comput. , 163 : 131 – 145 .
  • Ozis , T. and Ozdes , A. 1996 . A direct variational methods applied to Burgers’ equation . J. Comput. Appl. Math. , 71 : 163 – 175 .
  • Thomas , J. W. 1995 . Numerical Partial Differential Equations, Finite Difference Methods , New York : Springer .
  • Varoglu , E. and Finn , W. D. 1980 . Space-time finite elements incorporating characteristics for the Burgers’ equation . Int. J. Numer. Meth. Eng. , 16 : 171 – 184 .
  • Wood , W. L. 2006 . An exact solution for Burgers’ equation . Comm. Numer. Meth. Eng , 22 ( 7 ) : 797 – 798 .
  • Xie , S. , Li , G. , Yi , S. and Heo , S. 2010 . A compact finite difference method for solving Burgers’ equation . Int. J. Numer. Meth. Fluids , 62 : 747 – 764 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.