89
Views
8
CrossRef citations to date
0
Altmetric
Original Articles

Burgers equation : A study using method of lines

Pages 641-652 | Received 01 Jul 2015, Published online: 13 Sep 2016

References

  • H Bateman, 1915, Some Recent Researches on the Motion of Fluids, Mon. Weather Rev., 43, pp 163–170. doi: 10.1175/1520-0493(1915)43<163:SRROTM>2.0.CO;2
  • J M Burgers, 1939, Mathematical Examples illustrating Relations occurring in the Theory of Turbulent Fluid Motion, Trans. Roy. Neth. Acad. Sci. Amsterdam, 17,pp 1–53.
  • E Hopf, 1950, The Partial Differential Equation ut + uux – nuxx = 0, Commun. Pure Appl. Math., 9, pp 201–230. doi: 10.1002/cpa.3160030302
  • J D Cole, 1951, On a quasilinear parabolic equation occurring in Aerodynamics, Quart.Appl. Math., 9,pp 225–236.
  • W Malfiet, W Hereman, 1996, The Tanh Method-I. Exact Solutions of Nonlinear Evolution and Wave Equations, Physica Scripta, 54, pp 563–568. doi: 10.1088/0031-8949/54/6/003
  • Z Fu, S Liu, S Liu, 2002, New Transformation and New Approach to find Exact Solutions to Nonlinear Equations, Physics Letters A, 299, pp 507–512. doi: 10.1016/S0375-9601(02)00737-5
  • M L Wang, X Li, J Zhang, 2008, The G’/G expansion method and Travelling wave solutions of Nonlinear Evolution Equations, Physics Letters A, 272(4), pp 417–423. doi: 10.1016/j.physleta.2007.07.051
  • E L Miller, 1996, Predictor-Corrector studies of Burgers Model of Turbulent Flow, M.S. Thesis, University of Delaware, Newark, DE.
  • Caldwell J, Smith P, 1982, Solutions of Burgers equation with a large Reynolds number, Appl. Math. Modelling, 6, 381. doi: 10.1016/S0307-904X(82)80102-9
  • Nguyen H, Reynen J, 1984, A space-time finite element approach to Burgers equation in numerical methods of nonlinear problems, vol.2, Proc. Int. Conf.,(Universidal Poltecnica de Barcelona) ed C Taylor et al. (Swansea: Pineridge)
  • Kakuda K, Tosaka N, 1990, The generalized boundary element approach to Burgers equation, Int. J. Numer. Methods Eng., 29, pp 245–61. doi: 10.1002/nme.1620290203
  • Arina R, Canuto C, 1993, A self-adaptive domain decomposition for the viscous/inviscid coupling in Burgers equation, J. Comp. Phy., 105, 290. doi: 10.1006/jcph.1993.1075
  • Bar-Yoseph P et al., 1995, Space-time spectral element methods for one-dimensional nonlinear advection-diffusion problems, J. Comp. Phy., 119, 62. doi: 10.1006/jcph.1995.1116
  • Kutluay S, Bahadir R, Ozdes A, 1999, Numerical solution of one-dimensional Burgers equation: explicit and exact -explicit finite difference methods, J. Comp. Appl. Math., 103, pp 251–61. doi: 10.1016/S0377-0427(98)00261-1
  • Xu M, Duan Q, 2001, A novel approach to Burgers equation, Comm. Numer. Math. Eng., 17, pp 789–96.
  • Ben-Yu Guo, J Shen, 2000, A Laguerre-Galerkin method for nonlinear partial differential equations on a semi infinite interval, Numer. Math., 86, pp 635–654. doi: 10.1007/PL00005413
  • Chun-Gang Zhu, R H Wang, 2009, Numerical solutions of Burgers equation by cubic B-spline quasi-interpolation, Appl. Math. Comp., 208, pp 260–272. doi: 10.1016/j.amc.2008.11.045
  • Siraj ul Haq et al., 2012, On the numerical solution of nonlinear Burger-type equations using meshless method of lines, Appl. Math. Comp., 218, pp 6280–6290. doi: 10.1016/j.amc.2011.11.106
  • I Dag et. al., 2005, A Numerical Solution of the Burgers equation using cubic B-splines, Appl. Math. and Comp., 163, pp 199–211. doi: 10.1016/j.amc.2004.01.028
  • S Abbasbandy, M T Darvishi,2005, A Numerical solution of Burgers equation by Time Descretization of Adomian’s Decomposition Method, Appl. Math. and Comp., 170, pp 95–102. doi: 10.1016/j.amc.2004.10.060
  • Hou-de Han et al., 2006, Artificial Boundary Method for Burgers equation using Nonlinear Boundary Conditions, J.C.M., 24(3), pp 295–304.
  • D Irk, 2009, Sextic B-Spline Collocation Method for the Modified Burgers Equation, Kybernetics, 38(9), pp 1599–1620. doi: 10.1108/03684920910991568
  • A Ozdes, E N Aksan, 2006, The method of lines solution of the Kortweg-de Vries equation for small times, Int. J. Contemp. Math. Sci., 1(13), pp 639–650. doi: 10.12988/ijcms.2006.06067
  • E N Aksan et al., 2008, The method of lines solution of the convection-diffusion equation, Int. J. Pure Appl. Math., 46(1), pp 65–71.
  • A I Singh, K S Bhamra, 2010, A Method to Find Exact Solutions to Nonlinear Partial Differential Equations, Int.J. of Comp and Appl. Math, 5(6), pp 783–788.
  • A I Singh, K S Bhamra,2012, A Numerical Approximation for Burgers equation, Int. J. of Comp. Sci.and Math, 4(1), pp 13–18.
  • A I Singh, K S Bhamra, 2012, Numerical Solution of Modified Burgers Equation for Small Times, J. of Appl. Math. and Fluid Mech., 4(3), pp 199–202.
  • John H Mathews, Numerical Methods for Mathematics, Science and Engineering, Second Edition, Prentice Hall of India Private Limited.

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.