References
1. Sari, M. and Gurarslan, G. A sixth-order compact
nite dierence scheme to the numerical solutions of
Burgers' equation", Appl Math Comput., 208, pp. 475{
483 (2009).
2. Wang, J. and Warnecke, G. Existence and uniqueness
of solutions for a non-uniformly parabolic equation", J.
Dier. Equations, 189, pp. 1{16 (2003).
3. Miller, E.L. Predictor-corrector studies of Burger's
model of turbulent
ow", MS Thesis, University of
Delaware, Newark, Delaware (1966).
4. Kutluay, S., Bahadir, A.R., and Ozdes, A. Numerical
solution of one-dimensional Burgers' equation: explicit
and exact-explicit nite dierence methods", J. Comput.
Appl. Math., 103, pp. 251{261 (1999).
5. Seydaoglu, M. An accurate approximation algorithm
for Burgers' equation in the presence of small viscosity",
J. Comput. Appl. Math., 344, pp. 473{481 (2018).
6. Bahadir, A.R. and Saglam, M. A mixed nite
dierence and boundary element approach to onedimensional
Burgers' equation", Appl. Math. Comput.,
160, pp. 663{673 (2005).
7. Sari, M., Tunc, H., and Seydaoglu M. Higher order
splitting approaches in analysis of the Burgers equation",
Kuwait J. Sci., 46(1), pp. 1{14 (2019).
8. Hopf, E. The partial dierential equation", Commun.
Pur. Appl. Math., 9, pp. 201{230 (1950).
9. Cole, J.D. On a quasi-linear parabolic equation in
aerodynamics", Q. Appl. Math., 9, pp. 225{236 (1951).
10. Talwar, J., Mohanty, R.K., and Singh, S. A new
algorithm based on spline in tension approximation
for 1D parabolic quasi-linear equations on a variable
mesh", Int. J. Comput. Math., 93, pp. 1771{1786
(2016).
11. Jiwari, R. A hybrid numerical scheme for the numerical
solution of the Burgers' equation", Comput. Phys.
Commun., 188, pp. 50{67 (2015).
12. Seydaoglu, M., Erdogan, U., and Ozis, T. Numerical
solution of Burgers' equation with higher order
splitting methods", J. Comput. Appl. Math., 291, pp.
410{421 (2016).
13. Korkmaz, A. and Dag, I. Polynomial based dierential
quadrature method for numerical solution of
nonlinear Burgers' equation", J. Franklin I., 248, pp.
2863{2875 (2016).
14. Bahadir, A.R. and Saglam, M. A mixed nite
dierence and boundary element approach to onedimensional
Burgers' equation", Appl. Math. Comput.,
160, pp. 663{673 (2005).
15. Egidi, N., Maponi, P., and Quadrini, M. An integral
equation method for the numerical solution of the
Burgers equation", Comput. Math. Appl., 76(1), pp.
35{44 (2018).
16. Inan, B. and Bahadir, A.R. An explicit exponential
nite dierence method for the Burgers' equation",
European International Journal of Science and Technology,
2(10), pp. 61{72 (2013).
17. Zeytinoglu, A., Sari, M., and Pasaoglu, B.A. Numerical
simulations of shock wave propagating by a hybrid
approximation based on high-order nite dierence
schemes", Acta Phys. Pol. A, 133, pp. 369{386 (2017).
18. Verma, A.K. and Verma, L. Higher order time integration
formula with application on Burgers' equation",
Int. J. Comput. Math., 92, pp. 756{771 (2015).
2870 H. Tunc and M. Sari/Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 2853{2870
19. Rouzegar, J. and Sharifpoor, R.A. A nite element
formulation for bending analysis of isotropic and orthotropic
plates based on two-variable rened plate
theory", Sci. Iran., 22(1), pp. 196{207 (2015).
20. Ak, T., Karakoc, S.B.G., and Biswas, A. Application
of Petrov-Galerkin nite element method to shallow
water waves model: modied Korteweg-de Vries equation",
Sci. Iran., 24(3), pp. 1148{1159 (2017).
21. Zendehbudi, G. Combination of projection and
Galerkin nite element methods to solve the problem
of free convection in enclosures with complex geometries",
Sci. Iran, 25(3), pp. 1189{1196 (2018).
22. Kutluay, S., Esen, A., and Dag, I. Numerical solutions
of the Burgers' equation by the least-squares quadratic
B-spline nite element method", J. Comput. Appl.
Math., 167, pp. 21{33 (2004).
23. Sari, M. and Tunc, H. An optimization technique
in analyzing the Burgers equation", Sigma Journal of
Engineering and Natural Sciences, 35(3), pp. 369{386
(2017).
24. Kutluay, S. and Esen, A. A lumped Galerkin method
for solving the Burgers equation", Int. J. Comput.
Math., 81(11), pp. 1433{1444 (2004).
25. Dag, I., Saka, B., and Boz, A. B-spline Galerkin
methods for numerical solutions of Burgers' equation",
Appl. Math. Comput., 166, pp. 506{522 (2005).
26. Aksan, E.N. An application of cubic B-spline nite
element method for the Burgers' equation", Therm.
Sci., 22(1), pp. 195{202 (2018).
27. Ak, T. An application of Galerkin method to generalized
Benjamin-Bona-Mahony-Burgers equation",
Adiyaman University Journal of Science, 8(2), pp. 53{
69 (2018).
28. Ak, T., Saha, A., and Dhawan, S. Performance of a
hybrid computational scheme on travelling waves and
its dynamic transition for Gilson Pickering equation",
Int. J. Mod. Phys. C, 30(4), pp. 1950028{1/17 (2019).
29. Mohammadi, R. Numerical approximation for viscous
Cahn-Hilliard equation via septic B-spline", Appl.
Anal. (2019). DOI: 10.1080/00036811.2019.1594200
30. Mukundan, V. and Awasthi, A. Ecient numerical
techniques for Burgers' equation", Appl. Math. Comput.,
262, pp. 282{297 (2015).
31. Aksan, E.N. Quadratic B-spline nite element
method for numerical solution of the Burgers equation",
Appl. Math. Comput., 174, pp. 884{896 (2006).
32. Tunc, H. Various nite element techniques for
advection-diusion-reaction processes", MSc Thesis,
Yildiz Technical University (2017).
33. Shao, L., Feng, X., and He, Y. The local discontinuous
Galerkin nite element method for Burgers equation",
Math. Comput. Model., 54, pp. 2943{2954 (2011).
34. Abazari, R. and Borhanifar, A. Numerical study
of the solution of the Burgers and coupled Burgers
equations by a dierential transformation method",
Comput. Math. Appl., 59, pp. 2711{2722 (2010).