THERMAL SCIENCE

International Scientific Journal

Authors of this Paper

External Links

Emine Nesligul Aksan

AN APPLICATION OF CUBIC B-SPLINE FINITE ELEMENT METHOD FOR THE BURGERS` EQUATION

ABSTRACT
It is difficult to achieve exact solution of non-linear PDE, directly. Sometimes, it is possible to convert non-linear PDE into equivalent linear PDE by applying a convenient transformation. Hence, Burgers’ equation replaces with heat equation by means of the Hope-Cole transformation. In this study, Burgers’ equation was converted to a set of non-linear ODE by keeping non-linear structure of Burgers’ equation. In this case, solutions for each of the non-linear ODE were obtained by the help of the cubic B-spline finite element method. Model problems were considered to verify the efficiency of this method. Agreement of the solutions was shown with graphics and tables.
KEYWORDS
Burgers` Equation, Cubic B-spline Functions, finite element method
PAPER SUBMITTED: 2017-06-13
PAPER REVISED: 2017-11-15
PAPER ACCEPTED: 2017-11-18
PUBLISHED ONLINE: 2018-01-07
DOI REFERENCE: https://doi.org/10.2298/TSCI170613286A
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2018, VOLUME 22, ISSUE Supplement 1, PAGES [S195 - S202]
REFERENCES
  1. Rektorys, K, The method of discretization in time and partial differential equations, D. Reidel Publishing Company, Holland 1982
  2. Cole, J.D., On a quasi-linear parabolic equation occurring in aerodynamics, Quart. Apply. Math. 9 ( 1951), pp. 225-236
  3. Öziş, T., et al., The semi-approximate approach for solving Burgers' equation with high Reynolds number, Appl. Math. Comput., 163 (2005), pp. 131-145
  4. Aksan, E.N., A numerical solution of Burgers' equation by finite element method constructed on the method of discretization in time, Appl. Math. Comput, 170, (2005), pp. 895-904
  5. Abbasbandy, S., et al., A numerical solution of Burgers' equation by modified Adomian method. Appl. Math. Comput. 163, (2005), pp. 1265- 1272
  6. Öziş, T., et al., Numerical solution of Burgers' equation by quadratic Bspline finite element. Appl. Math. Comput.,165, (2005) , pp. 237-249
  7. Öziş, T., et al., A direct variational methods applied to Burgers' equation. J. Comput. Appl. Math. 71, (1996) ), pp. 163-175
  8. Aksan, E.N., et al., A numerical solution of Burgers' equation. Appl. Math. Comput. 156, (2003) , pp.395-402
  9. Prenter, P.M., Splines and Variational Methods., John Wiley & Sons, New York, USA 1975
  10. Burden, R.L., et al., Numerical Analysis. Bob Pirtle, USA 2005
PDF VERSION [DOWNLOAD]
An application of cubic B-Spline finite element method for the Burgers` equation

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence