Have a personal or library account? Click to login

Numerical Solutions of the Modified Burgers’ Equation by Finite Difference Methods

Open Access
|Jun 2017

References

  1. E. Hopf, The partial differential equation Ut +UUx -nUxx = 0; Communications on Pure and Applied Mathematics, Vol. 3, pp. 201-30.10.1002/cpa.3160030302
  2. M. A. Ramadan and T. S. El-Danaf, Numerical treatment for the modified burgers equation, Matmematics and Computers in Simulation 70 (2005) 90-98.10.1016/j.matcom.2005.04.002
  3. M. A. Ramadan , T. S. El-Danaf and F. E.I. Abd Alaal, A numerical solution of the Burgers equation using septic B-splines, Chaos, Solitons and Fractals 26 (2005) 795-804.10.1016/j.chaos.2005.01.054
  4. B. Saka and I. Dag, A numerical study of the Burgers’ equation, Journal of the Franklin Institute 345 (2008) 328-348.10.1016/j.jfranklin.2007.10.004
  5. D. Irk, Sextic B-spline collocation method for the modified Burgers’ equation, Kybernetes, Vol. 38, No. 9, 2009, pp. 1599-1620.10.1108/03684920910991568
  6. R.S. Temsah, Numerical solutions for convection-diffusion equation using El-Gendi method, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 760-769.10.1016/j.cnsns.2007.11.004
  7. A. Griewank and T. S. El-Danaf, Efficient accurate numerical treatment of the modified Burgers’ equation, Applicable Analysis, vol. 88, No. 1, January 2009, 75-87.10.1080/00036810802556787
  8. A. G. Bratsos, An implicit numerical scheme for the modified Burgers’ equation, in HERCMA 2009 (9o Hellenic-European Conference on Computer Mathematics and its Applications), 24-26 September 2009, Athens, Greece.
  9. A.G. Bratsos, A fourth-order numerical scheme for solving the modified Burgers equation, Computers and Mathematics with Applications 60 (2010) 1393 1400.
  10. A. G. Bratsos and L. A. Petrakis, An explicit numerical scheme for the modified Burgers’ equation, International Journal for Numerical Methods in Biomedical Engneering, 2011, 27: 232-237.10.1002/cnm.1294
  11. T. Roshan and K. S. Bhamra, Numerical solutions of the modified Burgers’ equation by Petrov-Galerkin method, Applied Mathematics and Computation, 218 (2011) 3673-3679.
  12. P.M. Prenter, Splines and Variational Methods, John Wiley, New York, 1975.
  13. S. G. Rubin and R. A. Graves, A Cubic spline approximation for problems in fluid mechanics, Nasa TR R-436, Washington, DC, 1975.
  14. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd Edition, Clarendon Press, Oxford (1987).
DOI: https://doi.org/10.1515/jamsi-2017-0002 | Journal eISSN: 1339-0015 | Journal ISSN: 1336-9180
Language: English
Page range: 19 - 30
Published on: Jun 23, 2017
Published by: Sciendo
In partnership with: Paradigm Publishing Services
Publication frequency: 2 times per year

© 2017 Yusuf Ucar, Nuri Murat Yagmurlu, Orkun Tasbozan, published by Sciendo
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.